I'm stuck on this problem. Hope someone can give me help.
Let H be a normal subgroup of G, show that if then or
I think I need to construct an isomorphism, but I have no clue how to do it here.
this claim is false! (unless by and you mean something else!) here's a counter-example:
let be a prime number and define and also choose
see that is a normal subgroup of a little work shows that and
however, it can be shown that for any finite group any normal subgroup of and any we have either or