Question
Explicitly give the elements and structure of the group Sn / An, .
Answer :
Word Count : 248
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Skip in 10
For (n\ge 5), consider the symmetric group (S_n) of all permutations of ({1,2,\dots ,n}) and its alternating subgroup (A_n) consisting of all even permutations. The index of (A_n) in (S_n) is 2, so the quotient group (S_n/A_n) has exactly two elements, namely the two cosets [ A_n \quad\text{and}\quad \sigma A_n, ] where (\sigma) is any fixed odd permutation, for example the transposition ((1,2)). Thus the elements of
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Related Questions
heck whether is a subring of the ring
or not. If it is, check whether or not it is an ideal of the ring also. If I is not a subring of the ring, then provide a subring of the ring.
क) मान लीजिए कि तथा
Explicitly give the elements and structure of the group Sn / An, .
सिद्ध कीजिए कि (n बार)
और
.
सिद्ध कीजिए कि वलयों के रूप में, .
मान लीजिए कि . जाँच कीजिए कि D एक UFD है या नहीं।
दर्शाइए कि के अनंततः अनेक मान हैं जिनके लिए
में
अखंडनीय है।