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Hall and Blackburn made important contributions in the study of regular $p$-groups and $p$-groups of maximal class. From their work, one can understand that in the classification of groups of order $p^n$, we must have to make two main cases: $p\leq n$, and $p>n$. With this interest, I am searching more and more material to study small $p$-groups, and their classification. The books I referred are that of Berkovich (Groups of prime power order) and of Leedham-Green, McKay (Structure of groups of prime power order).

Beside these two main references, can one suggest other books/notes which contains study of $p$-groups of maximal class and regular $p$-groups?

(The book of Berkovich mentions one book in bibliography, that of A. Mann-Finite $p$-groups; but I couldn't find this book. Is this book or notes published?)

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  • $\begingroup$ I am also interested with the book by A Mann who do many contribution to p-groups. $\endgroup$
    – Wei Zhou
    Dec 19, 2012 at 10:50
  • $\begingroup$ The book Enumeration of Finite Groups by Blackburn, Neumann, and Venkataraman has a lot of information on $p$-groups. $\endgroup$
    – Richard Stanley
    Dec 21, 2012 at 17:45
  • $\begingroup$ I'd like to mention Chapters 3 and 8 in excellent Huppert's `Endliche Gruppen, I'. Their contents is not covered by mentioned above books. $\endgroup$
    – yakov
    Jun 28, 2016 at 16:53
  • $\begingroup$ Philip Hall, the creator of modern $p$-group theory, has wrote only three papers devoted to general theory of finite $p$-groups. Essential part of their contents is not appeared in existing books. $\endgroup$
    – yakov
    Jun 28, 2016 at 17:03

1 Answer 1

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It's true that at one time I thought of writing such a book, and even wrote a few chapters, but at the moment I'm not sure if I'll ever finish it, so I'm telling people asking about it not to hold their breath. It should be noted that the book Structure of Groups... mentioned in the question has two authors: Charles R. Leedham-Green and Sue McKay.

Avinoam Mann

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    $\begingroup$ @Prof. A. Mann. As you have given many beautiful results on $p$-groups, I fasciate your book on $p$-group. I am very glad even if I know the content of the few chapter you have written. $\endgroup$
    – Wei Zhou
    Dec 19, 2012 at 13:14
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    $\begingroup$ Dear Professor Mann, welcome on MathOverflow! $\endgroup$
    – Salvatore Siciliano
    Dec 19, 2012 at 15:54

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