Show that if or
, then
, for
.
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Let G be a group of order , with only two subgroups —
and itself. Find a minimal generating set for G. Also, find out whether n is a prime or a composite number, or can be either.
अतः, दर्शाइए कि यदि N, R की एक ऐसी गुणजावली है जिसका M एक उचित
दर्शाइए कि M, R की एक गुणजावली है।
Show that there are infinitely many values of for which
is irreducible in
.
Let G be a group of order 56. What are all its Sylow p-subgroups? Show that G is not simple, i.e., G must have a proper normal non-trivial subgroup.
मान लीजिए कि . जाँच कीजिए कि D एक UFD है या नहीं।
जाँच कीजिए कि वलय
का एक उपवलय है या नहीं। यदि है, तो जाँच कीजिए कि वह इस वलय की एक गुणजावली भी है या नहीं। यदि I इस वलय का एक उपवलय नहीं है, तो इस वलय का एक उपवलय दीजिए।