0
$\begingroup$

Let $N$ be a normal $p$-subgroup of finite centerless group $G$ such that $G/N\cong A_{5}$. Is it possible $G/N\cong \leq $Aut$(Z(N))$?

  • 0
    Background, origin of problem, ideas, insights, self work...?2012-10-22
  • 0
    Is this really the question you want? Every finite group is a subgroup of Aut(Z(N)) for some p-group N.2012-10-22
  • 0
    What does $\cong\le$ mean?2012-10-22
  • 0
    @DerekHolt "isomorphic to a subgroup" perhaps?2012-10-22
  • 0
    @DerekHolt: Isomorphic to a subgroup. This question related to my former question.2012-10-23
  • 0
    The answer is yes. It is not only possible, it is certain! Use the action by conjugation.2012-10-23

1 Answers 1