Berkovich, Yakov 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]. Reviewer: Shi Wujie (Chongqing) 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 Keywords:non-solvable finite groups; class numbers; numbers of conjugacy classes Citations:Zbl 0934.20008 × Cite Format Result Cite Review PDF