Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

can one suggest a survey article on automorphisms of $p$ groups, and automorphisms of abelian groups/ abelian $p$ groups?

share|cite|improve this question
For finite abelian groups, there is the paper "Automorphisms of Finite Abelian Groups" By Hillar and Rhea, AMM 114 (2007), 917--923. For general p-groups, a lot can be said. There is a whole book(s) on the subject by Khukhro, and you can find alot of information in the two volumes of Berkovich. – user641 Apr 12 '11 at 18:59

I second the recommendations of Steve D. in his comment: the paper of Hillar and Rhea and Khukhro's book are both excellent. The two volumes of Berkovich (and Janko for vol. 2) are, as Steve says, full of information but I have found that they do not make for a particularly enjoyable read.

You might also want to look at: "A survey on automorphism groups of finite p-groups" by Geir Helleloid and "Class preserving automorphisms of finite p-groups: A survey" by Manoj Yadav. I think there are copies of both of these on the Arxiv.

The paper "Some questions about p-groups" by A. Mann has a section discussing some open problems about automorphisms of finite p-groups & is well worth a read.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.