AUTOMORPHISM CRITERIA FOR M*-GROUPS

Abstract

AbstractWe prove that the determination of all $M^*$-groups is essentially equivalent to the determination of finite groups generated by an element of order 3 and an element of order 2 or 3 that admit a particular automorphism. We also show how the second commutator subgroup of an $M^*$-group $G$ can often be used to construct $M^*$-groups which are direct products with $G$ as one factor. Several applications of both methods are given.AMS 2000 Mathematics subject classification: Primary 20D45; 20E36. Secondary 14H37; 30F50