Squares of real conjugacy classes in finite groups

Abstract

[EN] We prove that if a finite group G contains a conjugacy class K whose square is of the form 1¿D, where D is a conjugacy class of G, then ¿K¿ is a solvable proper normal subgroup of G and we completely determine its structure. We also obtain the structure of those groups in which the assumption above is true for all non-central conjugacy classes and when every conjugacy class satisfies that its square is the union of all central conjugacy classes except at most one.

[ES] Probamos que si un grupo finito G contiene una clase de conjugación K cuyo cuadrado es unión 1 y D, siendo D una clase de conjugación de G, entonces el subgrupo generado por K es resoluble y normal en G. También se determinan otras propiedas estructurales del grupo. those groups in which the assumption above is true for all non-central conjugacy classes and when every conjugacy class satisfies that its square is the union of all central conjugacy classes except at most one.