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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Qn no. 3 and 5
3 Let G be a finite group then (a) Gis abelian if O(G)= pg where p and q distinct primes b) Gis abelian if every non identiy element of G is of order 2 shal G (C)Gis abelian if the quotient group 7 is cyclic, Z(G) is centre ofG Let G be a cyclic group of order 12. Then the number of nonn isomorphic subgroups of G is Mathema 5 Suppose N is a normal subgroup of G which one of the following is true? (b) IfG is non abelian group then is a non abelian stitut group. O. (C G (a) If G is infinite group thenis an infinte group. G G )IfGis cyclic thenis an abelian group. (d) If G is abelian group thenis a cyclic G
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