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Jan 26, 2015 at 22:28 history edited Geoff Robinson CC BY-SA 3.0
typo
Jul 10, 2014 at 20:52 comment added Geoff Robinson The following (accurate) text was inserted into my answer by Peter Mueller, and should probably be given as a comment: Added (answering Shahryari's question from the comments): For each odd prime $p$ Heineken and Liebeck (see Section 3) construct many $p$-groups of class $2$ whose full automorphism group is a $p$-group.
Jul 10, 2014 at 20:51 history edited Geoff Robinson CC BY-SA 3.0
deleted text inserted by Peter Mueller
Jul 10, 2014 at 20:50 vote accept Sh.M1972
Jul 11, 2014 at 0:34
Jul 10, 2014 at 15:07 history edited Geoff Robinson CC BY-SA 3.0
typos
Jul 10, 2014 at 14:58 history edited Geoff Robinson CC BY-SA 3.0
added condition on $p$-group.
Jul 10, 2014 at 14:51 history edited Geoff Robinson CC BY-SA 3.0
added 55 characters in body
Jul 10, 2014 at 8:52 comment added Derek Holt For example, there is a group of order $3^6$, $\mathtt{SmallGroup}(729,31)$ with automorphism group of roder $3^9$ and a unique central element of order $3$.
Jul 10, 2014 at 8:48 history edited Peter Mueller CC BY-SA 3.0
added 297 characters in body
Jul 10, 2014 at 8:10 comment added Sh.M1972 I find the gap in my proof so I am going to edit the question. But I am not sure if there exists such a $p$-group you talk about in the answer. Is there really a $p$-group of class 2 with automorphism group a $p$-group?
Jul 10, 2014 at 6:57 history answered Geoff Robinson CC BY-SA 3.0