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Non-solvable groups with a large fraction of involutions. (English) Zbl 0945.20009

Deshouillers, Jean-Marc (ed.) et al., Structure theory of set addition. Paris: Société Mathématique de France, Astérisque. 258, 241-248 (1999).
Let \(k(G)\) be the number of conjugacy classes of a finite group \(G\) and \(\text{mc}(G)=k(G)/|G|\). In this paper, the author classifies the non-solvable finite groups \(G\) with \(\text{mc}(G)\geq 1/16\). The proof of this theorem depends on previous works of the author and E. M. Zhmud’ [Characters of finite groups, Part 1, Am. Math. Soc., Providence, RI (1998; Zbl 0934.20008)]. Some consequences are derived as well.
For the entire collection see [Zbl 0919.00044].

MSC:

20D05 Finite simple groups and their classification
20D60 Arithmetic and combinatorial problems involving abstract finite groups
20C15 Ordinary representations and characters
20E45 Conjugacy classes for groups

Citations:

Zbl 0934.20008