Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Many theorems about odd order $p$-groups fail miserably for $2$-groups. These can range from simple $2$-group exceptions (e.g. Frobenius complements can be either cyclic or generalized quaternion) to full blown analogs proved with vastly different, "$2$-groupy" techniques (e.g. Glauberman's $\text{ZJ}$ theorem vs. Stellmacher's results about $\Sigma_4$-free groups.) It's clear that $2$-groups in some way work fundamentally differently than other $p$-groups, and I would like to improve my understanding of exactly how.

Does anyone know of a comprehensive reference compiling important results about $2$-groups specifically? Is there a book or survey article about the theory of $2$-groups out there somewhere?

I would be especially interested in sources discussing differences in the internal structure of $2$-groups, rather than differences associated with their place in finite groups, such as my examples above. (And again, I don't need any references for $p$-groups in general - I've got plenty of those.)

share|improve this question
Berkovich and Janko, while ostensibly about $p$-groups in general, devote more than half their three books to results on $2$-groups. –  user641 Mar 1 '13 at 7:42
This is a good question. I too have many times been amazed at how different $p$-groups behave when $p=2$ (a good example where the complications show up en masse is the classification of $p$-groups all of whose non-normal subgroups are cyclic, which is chapter 16 in Berkovich). –  Tobias Kildetoft Mar 1 '13 at 14:22

Your Answer


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

Browse other questions tagged or ask your own question.