Zoltán Halasi, Attila Maróti, Said Sidki, Marcelo Bezerra
June 29, 2012
Abstract. A finite group G is called expansive if for every normal set S and every conjugacy class C of G the normal set consists of at least as many conjugacy classes of G as S does. This notion is motivated by a finiteness criterion. It is shown that a group is expansive if and only if it is a direct product of expansive simple or abelian groups. The groups and are expansive for every and every respectively. Many small simple groups including all sporadic simple groups are also expansive.