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

The MathSciNet review of the book Berkovich, Zhmud, Characters of finite groups. Part 2, says the following:

...Let $k(G)$ be the number of conjugacy classes of the group $G$, $T(G)$ the sum of the degrees of its irreducible characters and $t(G)$ the number of its involutions. Chapter 28 characterizes the groups with $k(G)\ge 1/16|G|$, the groups with $T(G)\ge 1/4|G|$ and the groups with $t(G)\ge 1/4|G|$....

Since I cannot get a hold of the book soon, I would appreciate if someone could briefly list these results, and/or give me the original references where these problems are addressed.

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.