THE EMBEDDING OF A CYCLIC PERMUTABLE SUBGROUP IN A FINITE GROUP. II

Abstract

AbstractIn two previous papers we established the structure of the normal closure of a cyclic permutable subgroup $A$ of a finite group, first when $A$ has odd order and second when $A$ has even order, but with an extra hypothesis that was unnecessary in the odd case. Here we describe the most general situation without any restrictions on $A$.AMS 2000 Mathematics subject classification: Primary 20D35; 20D40