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Two-transitive actions on conjugacy classes

Published online by Cambridge University Press:  17 April 2009

Michael J.J. Barry  and
Michael B. Ward
Michael J.J. Barry
Affiliation:
Department of MathematicsAllegheny CollegeMeadville PA 16335, United States of America e-mail: [email protected]
Michael B. Ward
Affiliation:
Department of MathematicsWestern Oregon UniversityMonmouth OR 97361, United States of America e-mail: [email protected]
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Abstract

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Every group acts transitively by conjugation on each of its conjugacy classes of elements. It is natural to wonder when this action becomes multiply transitive. In this paper, we determine all finite groups which act faithfully and 2-transitively on a conjugacy class of elements. We also give some consequences including a solvability criterion based on what fraction of elements belong to conjugacy classes upon which the group acts faithfully and 2–transitively.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 409 - 420
Copyright
Copyright © Australian Mathematical Society 1999

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