Timeline for Two $p$-groups whose automorphism groups have isomorphic Sylow $p$-subgroups

6 events

when toggle format	what		by	license	comment
Apr 7, 2014 at 21:37	comment	added	Marty Isaacs		You have probably already checked this, but Magma says that for p=3 and n=1, the groups are isomorphic.
Apr 7, 2014 at 19:15	history	edited	Yassine Guerboussa	CC BY-SA 3.0	added 11 characters in body
Apr 7, 2014 at 19:14	comment	added	Yassine Guerboussa		Ok, It is my mistake that I didn't noticed that $M$ is not abelian.
Apr 7, 2014 at 19:12	comment	added	Yassine Guerboussa		@Jared: thanks for your comment; You may notice that $M$ is not abelian, so that $M \times E_n$ and $E_{n+3}$ cannot be isomorphic.
Apr 7, 2014 at 17:39	comment	added	Jared		Perhaps I'm not understanding the question, but it seems to me that $M\times E_n\cong E_{n+3}$. Viewing $E_{n}$ as a vector space over $\mathbb{F}_p$, we then have the isomorphism of groups $\mathrm{Aut}(E_n)\cong\mathrm{GL}(n,p)$ for all $n$.
Apr 7, 2014 at 10:22	history	asked	Yassine Guerboussa	CC BY-SA 3.0