Thread: quotient groups

question: Give an examples of a group G and a normal subgroup N satisfying the following properties; or if no example exists, state that. In either case, justify answers.

(a)G is abelian, and G/N is non-abelian
(b)G is cyclic, and G/N is not cyclic
(c)G/N is not isomorphic to any subgroup G.

could anyone help me with this problem??? please?

Originally Posted by jin_nzzang

question: Give an examples of a group G and a normal subgroup N satisfying the following properties; or if no example exists, state that. In either case, justify answers.

(a)G is abelian, and G/N is non-abelian
(b)G is cyclic, and G/N is not cyclic
(c)G/N is not isomorphic to any subgroup G.

could anyone help me with this problem??? please?

no example exists for (a) and (b). for (c) an example is and

Hi
thanks a lot for your help,, but could you please justify the answers so that i can understand it better? (at least one of them as an example ? )

Originally Posted by jin_nzzang

Hi
thanks a lot for your help,, but could you please justify the answers so that i can understand it better? (at least one of them as an example ? )

Remember that your quotient group acts very much like your group - it has multiplication .

So, if the group is abelian then .