Solvable and supersolvable groups in which every element is conjugate to its inverse

J. Lennart (John) Berggren

Vol. 37 (1971), No. 1, 21–27

DOI: 10.2140/pjm.1971.37.21

Abstract

Let S be the class of finite groups in which every element is conjugate to its inverse. In the first section of this paper we investigate solvable groups in S: in particular we show thal if G ∈ S and G is solvable then the Carter subgroup of G is a sylow 2-subgroup and we show that any finite solvable group may be embedded in a solvable group in S. In the second section the main theorem reduces the study of supersolvable groups in S to the study of groups in S whose orders have the form 2^αp^β,p an odd prime.

Mathematical Subject Classification 2000

Primary: 20D10

Milestones

Received: 10 February 1970

Published: 1 April 1971