Timeline for The parity of the full automorphism group order of finite non-abelian groups of prime exponent

11 events

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Jan 20, 2016 at 15:58	comment	added	Shahrooz		Also, 32000 groups of order $5^7$ is tested and there is not such example. Only one group with odd order automorphism exist, but the exponent of this group is $125$.
Jan 19, 2016 at 12:23	vote	accept	Alireza Abdollahi
Jan 19, 2016 at 12:22	comment	added	Alireza Abdollahi		@YCor. There is no example of order $3^7$.
Jan 19, 2016 at 12:16	comment	added	Alireza Abdollahi		@YCor. There is also no such group of order $5^6$. Note that all groups of exponent $3$ and of order at most $3^6$ is of class at most $2$.
Jan 19, 2016 at 12:08	comment	added	Alireza Abdollahi		@YCor. I have done it for all non-abelian groups of exponent $3$ of order at most $3^6$. There is no such example among such groups.
Jan 19, 2016 at 11:51	comment	added	YCor		Did you do any computer verification (in view of my answer, I'd be interested in a checking for groups of order $3^4$, $3^5$, $3^6$, $5^6$ expecting there are no examples, and would expect an example in order $p^7$ or $p^8$ for some $p$)?
Jan 18, 2016 at 12:28	history	edited	Stefan Kohl♦	CC BY-SA 3.0	Fixed a typo in the title.
Jan 18, 2016 at 12:06	answer	added	YCor		timeline score: 13
Jan 18, 2016 at 11:56	history	edited	YCor		edited tags
Jan 18, 2016 at 11:56	comment	added	YCor		I added the Lie algebra tag, because a $p$-group of exponent $p$ and nilpotency length $<p$ can be viewed as a Lie algebra by Malcev correspondence.
Jan 18, 2016 at 6:45	history	asked	Alireza Abdollahi	CC BY-SA 3.0