MathOverflow is a question and answer site for professional mathematicians. 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

How can one estimate the number of $p$-groups of order $\leq p^n$ that split over a normal abelian subgroup?

Moreover, let $s(n,p)$ be the number of such groups, and let $f(n,p)$ denotes the number of $p$-groups of order $\leq p^n$.

What can one expect for $\frac{s(n,p)}{f(n,p)}$?

Is it true that $lim_n\frac{s(n,p)}{f(n,p)}$ is 0, for every prime $p$?

share|cite|improve this question

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.