Vol. 37, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
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