Define , a finite -group, such that isn't abelian. Let such that , where is abelian....

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Define , a finite -group, such that isn't abelian. Let $K \le G$ such that |G:K| = p , where is abelian.

Prove that there are either or p + 1 such abelian subgroups, and if there are p + 1 , then the index of Z(G) in is p^2

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solution in we lenow a is finite group a O(C) = pa, p-group led G= Oo . 3 o(G) = B = 2 then G = 28 is 2-grouß; aus 0g = {ts, if G + 20 then it will have only centre elemann subgroup which will is either There 1 cute such pt 1 abelian enbroup: it Ther

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Define , a finite -group, such that isn't abelian. Let such that , where is abelian....