The largest lengths of conjugacy classes and the Sylow subgroups of finite groups

Research paper by Liguo He, Wujie Shi

Indexed on: 01 Jan '06Published on: 01 Jan '06Published in: Archiv der Mathematik


Let G be a finite nonabelian group, P ∈Sylp(G), and bcl(G) the largest length of conjugacy classes of G. In this short paper, we prove that in general and |P/Op(G)| < bcl(G) in the case where P is abelian.