Question

give an example of subgroup of G ,which is not characteristics ( where G is a group).​

Answer 1

Answer:

Ok sure mate

Therefore, K1 and K2 are both normal subgroups of G that are not characteristic. When K=Z2 is the cyclic group of order two, G=Z2×Z2 is the Klein four-group. In particular, this gives a counterexample where the ambient group is an abelian group.

Answer 2

Answer:

Therefore, K1 and K2 are both normal subgroups of G that are not characteristic. When K=Z2 is the cyclic group of order two, G=Z2×Z2 is the Klein four-group. In particular, this gives a counterexample where the ambient group is an abelian group