Vol. 37, No. 1, 1971

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

J. Lennart (John) Berggren

Vol. 37 (1971), No. 1, 21–27

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 2αpβ,p an odd prime.

Mathematical Subject Classification 2000
Primary: 20D10
Received: 10 February 1970
Published: 1 April 1971
J. Lennart (John) Berggren