IGNOU MSCMACS MMT 3 Algebra Solved Assignment English

Looking for the solved assignment for MMT 3Algebra? Here you can get the complete solved assignment in PDF format for your IGNOU course.

If you are preparing your assignment and need the answers in one place, this solved PDF can help you save time and understand how the questions can be answered. You can read it on your mobile, save it for later, or take a print if required.

MSCMACS 2026 - English

Before you order: Please check the course code, subject code, year and session with your assignment before purchasing.

MMT 3: Algebra

High Demand Verified Solution

★★★★★ 4.9/5 (91 Students)

₹80 ₹30

63% OFF You Save: ₹50

Language

Type

Choose Your Assignment (latest Selected) Check Question Included See Included Question

Title Name	IGNOU MSCMACS MMT 3 Algebra Solved Assignment English
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	MASTER DEGREE PROGRAMMES
Course Code	MSCMACS
Course Name	M.Sc. Mathematics with Applications in Computer Science
Subject Code	MMT 3
Subject Name	Algebra
Year	2026
Session	-
Language	English
Assignment Code	MMT 3/Assignment-1/2026
Product Description	Assignment of MSCMACS (M.Sc. Mathematics with Applications in Computer Science) 2026. Latest MMT 03 2026 Solved Assignment Solutions
Format	Ready-to-Print PDF (.soft copy)

Need Help With This Assignment?

Looking for the solved assignment for this subject? You can get the complete solved PDF and use it while preparing your assignment.

✓ Complete Solved Assignment — Questions with their answers in one PDF.

✓ Save Your Time — No need to search different websites for every question.

✓ Easy to Read — Keep the PDF on your phone or take a print when required.

✓ Get It Online — Download your assignment after successful payment.

✓ Useful for Preparation — Read the answers and prepare your assignment with less hassle.

Just check once before buying: Make sure the Course Code, Subject Code, Year and Session shown above match your assignment.

📋 Assignment Content Preview

Please make sure your assignment questions match your current IGNOU session

MMT 3 2025 - English

Course Code: MMT-003

Assignment Code:MMT-003/TMA/2025

Maximum Marks: 100

1. Which of the following statements are true and which are false? Give reasons for your answer.

(a) If a finite group G acts on a finite set S, then G_s1 = G_s2 for all s₁, $₂ ∈ X.

(b) There are exactly 8 elements of order 3 in S₄.

(d) $F_7(sqrt{3})=F_7(sqrt{5})$

(e) For any $ainmathbb{F}_{2^5}^*,quad a e 1,quadmathbb{F}_{2^5}=mathbb{F}_2[a]$

2. (a) Consider the natural action of GL₂ $left(mathbb{R} ight)$ on M₂ $left(mathbb{R} ight)$ , the set of 2 x 2 real matrices, by left multiplication.

(i) Under this action, if det(x) ≠ 0, show that the stabiliser of x ∈ M₂ $left(mathbb{R} ight)$ is {I}, where I is the 2 x 2 identity matrix.

(ii) Suppose that det(x) = 0 in the remaining parts of this exercise. We will show that the stabiliser of x is infinite. If x = 0, the stabiliser of x is GL₂ $left(mathbb{R} ight)$ . So suppose x ≠ 0. Let us write $X=egin{bmatrix}a&c\b&dend{bmatrix}.$ Then, $egin{bmatrix}a\bend{bmatrix}=lambdaegin{bmatrix}c\dend{bmatrix}$ for non-zero λ ∈ R. Why?

(iii) Let $egin{bmatrix}a'\b'end{bmatrix}$ be a vector that is not a scalar multiple of $egin{bmatrix}a\bend{bmatrix}$ . Show that there is a matrix b = $egin{bmatrix}u&v\w&zend{bmatrix}$ such that b $egin{bmatrix}a\bend{bmatrix}$ = 0 and b $egin{bmatrix}a'\b'end{bmatrix}$ = α $egin{bmatrix}a'\b'end{bmatrix}$ (Hint: Set up two sets of simultaneous equations in two unknowns and argue why they have a solution.)

(iv) Check that I-b is in the stabiliser of x. Also, show that there are infinitely many choices of a for which I - b is invertible.

(b) Let H be a finite group and, for some prime p, let P be a p-Sylow subgroup of H which is normal in H. Suppose H is normal in K, where K is a finite group. Then, show that Pis normal in K.

3. Describe the set of primes p for which x² - 11 splits into linear factors over Zp.

4. (a) Determine, up to isomorphism, all the finite groups with exactly 2 conjugacy classes.

(b) Is there a finite group with class equation 1+1+2+2+2+2+2+2?

(i) $left(frac{173}{211} ight)$ (ii) $left(frac{167}{239} ight)$

5. (a) Let ? (?) be a finite extension F of odd degree(greater than 1). Show that ? (?²) = ? (?).

(b) Let ? ⊂ ? and let ?, ? ∈ ? be algebraic over F of degree m and n, respectively. Show that [? (?, ?) ∶ ? ] ≤ ??. What can you say about [? (?, ?) ∶ ? ] if m and n are coprime?

6. (a) If char(F) ≠ 2, show that a polynomial ax² + bx + c is irreducible iff $b^2-4ac otinmathbb{F}^{*2}$ where $mathbb{F}^{*2}$ is the group of squares in $mathbb{F}$ .

(b) By looking at the factorisation of x⁹ - x ∈ $mathbb{F}_{3}$ [x] guess the number of irreducible polynomials of degree 2 over $mathbb{F}_{3}$ . Find all the irreducible polynomials of degree 2 over $mathbb{F}_{3}$ .

(c) If Fis a finite field show that there is always an irreducible polynomial of the form x³ - x + a where a ∈ F.(Hint: Show that $xmapsto x^3-x$ is not a surjective map.)

7. (a) Suppose that $M=egin{bmatrix}A&B\C&Dend{bmatrix}$ is 2n × 2n matrix where A, B, C and D are nxn matrices. Show that M is symplectic if and only if the following conditions are satisfied:

A^tD - C^tB 1

A^tC - C^tA = 0

B^tD-D^tB = 0

(Hint: Use block matrix multiplication.)

Also, check that the matrix $egin{bmatrix}0&-A\A&0end{bmatrix}$ where A is a n x n orthogonal matrix, is a symplectic matrix

(b) The aim of this exercise is to show that SP₂ $left(mathbb{R} ight)$ acts transitively on $mathbb{R}^{2}$ {0}.

(i) Show that a matrix $egin{bmatrix}a&b\c&dend{bmatrix}in GL_2(mathbb{R})$ is symplectic if and only if ad - bc = 1.

(ii) Show that, to prove that SP₂ $left(mathbb{R} ight)$ acts transitively on GL₂ $left(mathbb{R} ight)$ , it is enough to show that, for any vector $egin{bmatrix}a\bend{bmatrix} emathbf{0}inmathbb{R}^2$ , there is a 2 x 2 symplectic matrix with $egin{bmatrix}a\bend{bmatrix}$ as the first column . (Hint: For any matrix A, what is $A,,frac{1}{2}$ ?)

(iii) Complete the proof by showing that, given any non-zero $egin{bmatrix}a\bend{bmatrix}$ vector non-zero vector, there is always a $egin{bmatrix}a'\b'end{bmatrix}$ such that $egin{bmatrix}a&a'\b&b'end{bmatrix}$ is symplectic.

8. In this exercise, we ask you to find the Sylow ?-subgroups of the dihedral group

$D_n=langle x,y:x^n,y^2,yxyx angle,quad ninmathbb{N},nge 2.$

(a) Let p be an odd prime that divides n, n = p^r l, p + 1. Suppose C = (x¹). Show that C is the unique Sylow p-subgroup of D_n.

(b) Prove the relation

$y^j x^k y^l=egin{cases}y^j x^{j+l}& ext{if k is even}\y^{j+k}x^l& ext{if k is odd}end{cases}$

Further, find all the elements of order 2 in D_n.

(d) Suppose n is even, n = 2^km, where 2 + m, k ≥ 2. Let N = (x^m) and H = (y). Show that H N is a subgroup of D_n. What is its order?

(e) Suppose n is as in the previous part. Find all the Sylow 2-supgroups of D_n. Describe them in terms of x and y.

(a) Let $G=langle a,bmid a^2,b^3,aba^{-1}b^{-1} angle$ . Show that G is the cyclic group of order six.

(b) Solve the following set of congruences:

$xequiv 2pmod{17}$

$3xequiv 4pmod{19}$

$xequiv 7pmod{23}$

Question no.	Block 1	Block 2	Block 3	Block 4	Block 5
2 a)	5
2 b)	3
2 c)		2
3 c)			10
4 a)	4
4 b)	3
4 c)			3
5 a)				2
5 b)				5
5 c)				3
6 a)				2
6 b)				6
6 c)				2
7 a)		4
7 c)		1
7 c)		3
7 c)		2
8 a)	3
8 b)	4
8 c)	2
8 d)	3
8 e)	3
9 a)		5
9 b)			5
9 c)			5
Total	30	17	23	20	0

❓ Frequently Asked Questions (FAQs)

Q: How will I receive the PDF?
A: Immediately after payment, the download link will appear.

Q: Is this hand-written or typed?
A: This is a professional typed computer PDF. You can use it as a reference for your handwritten submission.

➕Other Details

IGNOU MMT 3 Solved Assignment 2026 – Prepare Smarter, Save Valuable Time

Searching for the 2026 IGNOU MMT 3 Solved Assignment? Get a ready-to-use reference for MMT 3 - Algebra and make your assignment preparation simpler, faster and more organised. Our carefully prepared MMT 3 Algebra Solved Assignment is designed to help you understand the questions, study the important points and prepare your assignment answers with greater confidence.

Why spend hours searching through different sources when you can have your MMT 3 solved assignment reference available in one convenient resource? Whether you are studying after work, preparing several IGNOU subjects together or simply want a dependable reference, this material can save you valuable preparation time.

MMT 3 2026 Solved Assignment – What You Get

Latest 2026 assignment reference for MMT 3 Algebra
Question-wise answers arranged for easy study and reference
Clear and student-friendly presentation for easier understanding
English language version available
Digital soft copy / PDF for convenient access
Useful reference material for preparing your own assignment answers
Helps you identify important points, answer structure and relevant content

Stop Struggling With Every Question. Start Preparing With a Better Reference.

Assignment preparation can become time-consuming when you have multiple subjects, limited study hours and a long list of questions to complete. A good reference can help you move from “What should I write?” to “Now I understand how to prepare this answer.”

The IGNOU MMT 3 Solved Assignment 2026 gives you a convenient study reference so you can review the questions, understand the expected subject matter and organise your own answers more efficiently.

Study less randomly. Prepare more systematically. Keep the reference with you while working on your assignment and use it whenever you need help understanding a question or arranging the important points.

Get Your MMT 3 Algebra Solved Assignment 2026

Course: M.Sc. Mathematics with Applications in Computer Science (MSCMACS)
Subject: MMT 3 - Algebra
Session: January 2026 - December 2026
Language: English

Need the Help Book / Solved Assignment?
Call us: 9199852182 / 9852900088
WhatsApp: 9199852182

Your Time Matters – Make Assignment Preparation Easier

If you are balancing IGNOU studies, work, family responsibilities or other subjects, every hour of study matters. Having a structured reference beside you can make it easier to understand the assignment and focus your time on preparing your own submission.

Instead of repeatedly searching for answers across different websites and sources, keep your MMT 3 Algebra Solved Assignment 2026 ready for reference whenever you study.

A Useful Reference for Your IGNOU Assignment Preparation

Understand the question → Find the relevant points → Study the answer → Prepare your own assignment with confidence.

IGNOU MSCMACS Assignments 2026

The MSCMACS (M.Sc. Mathematics with Applications in Computer Science) programme includes assignment work as part of the academic requirements applicable to students. Students should always verify the latest assignment questions, instructions and submission requirements from the official IGNOU website.

Our MMT 3 Solved Assignment is independently prepared reference material intended to assist students with understanding and preparing their answers. It is not an official IGNOU publication.

Why Keep a Solved Assignment Reference?

A useful reference is more than simply a collection of answers. It can help you see how a question can be approached, what important points need attention and how the subject matter can be organised into a clear answer.

Save preparation time with organised reference material
Understand difficult questions more easily
Review important concepts before writing your answers
Improve answer organisation with a structured reference
Study conveniently whenever and wherever you need it

Product Information

Course Name	M.Sc. Mathematics with Applications in Computer Science
Course Code	MSCMACS
Subject Code	MMT 3
Subject	Algebra
Programme	MASTER DEGREE PROGRAMMES Courses
Language	English
Material Type	Solved Assignment – Soft Copy / PDF

Ready to Make Your MMT 3 Assignment Preparation Easier?

Get the 2026 MMT 3 Algebra Solved Assignment as a convenient reference for your assignment preparation.

Call: 9199852182 / 9852900088
WhatsApp: 9199852182

IGNOU MMT 3 2026 Solved Assignment
Get your reference copy and start preparing with confidence.

Important Note for IGNOU Students

Always check the latest assignment questions and submission instructions on the official IGNOU website before preparing and submitting your assignment. Use this solved assignment as a study and reference resource and prepare your own submission according to the applicable IGNOU requirements.

Why Choose IGNOU Academy for Your Assignments?

Getting your assignments right is an important part of your IGNOU academic journey.IGNOU Academy provides carefully prepared reference materials designed to makeassignment preparation simpler, clearer and more convenient for students.

Latest Curriculum: Materials are prepared with the current IGNOU syllabus and assignment requirements in mind.
Proper Assignment Format: Understand the structure, presentation and answer style generally expected in an IGNOU assignment.
Simple Explanations: Difficult topics are explained in clear and easy-to-understand language.
Exam Preparation: Assignment material can also be useful for revising important concepts before the Term-End Examination.
Student-Friendly Language: Clear English/Hindi content helps students understand topics without unnecessary complexity.
Trusted by IGNOU Learners: Students across India use IGNOU Academy as a convenient source of assignment and study-reference material.

These materials are provided as reference study guides. Students should understandthe concepts, follow IGNOU guidelines and prepare their own original assignmentswhere required.

How to Get Your Solved Assignment PDF

Visit IGNOU Academy:Go to www.ignouacademy.com.
Find Your Course:Search for your programme, course code and subject.
Select the Session:Choose the latest available reference material for your academic session.
Complete Your Order:Add the required material to your cart, log in or register, and complete the payment.
Access Your Material:After successful payment, access your purchased study material from your account.

Step-by-Step: Finding IGNOU Assignment Question Papers

Open the Website:Visit www.ignouacademy.com.
Open Assignment Question Papers:Select the relevant IGNOU assignment question paper section.
Filter Your Requirement:Select your course, session and medium such as English or Hindi.
Open the Paper:View or download the required question paper for your preparation.

How to Submit Your IGNOU Assignments

Prepare Neatly:Use the format and submission instructions applicable to your programme and study centre.
Complete the Front Page:Enter your Name, Enrollment Number, Programme/Course Code, Subject and Study Centre details correctly.
Offline Submission:If your study centre requires physical submission, submit the assignment as instructed and retain the acknowledgement.
Online Submission:Where online submission is permitted, follow the instructions issued by your Regional Centre or Study Centre. Keep proof of submission for your records.

Tracking Your Assignment Submission Status

After submitting your assignments, students can check whether their assignmentmarks and submission details have been updated through the applicable official IGNOU system.

Open the Official IGNOU Student Area:Visit the official IGNOU website and access the relevant student services.
Find Assignment Status:Open the assignment-status service applicable to your programme.
Enter Your Details:Provide your Enrollment Number and other requested programme details.
Check the Status:Review the available submission, evaluation and marks information.

A Quick Tip for IGNOU Students

Assignments are an important part of the IGNOU evaluation process. Preparing themcarefully, understanding the questions, following the prescribed format and submittingthem within the applicable deadline can help you stay on track academically.

Smart Study + Proper Preparation + Timely Submission = Better Academic Planning

Need Help? Contact IGNOU Academy WhatsApp: +91 9199852182 | Website: www.ignouacademy.com

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers