Two-Transitive Actions on Conjugacy Classes

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1999
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Barry, Michael J. J.
Ward, Michael B.
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Abstract
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.
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Mathematics
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This version of this article was selected for publishing by the Bulletin of the Australian Mathematical Society © 1999 Barry and Ward.
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Barry, M.J.J. and Ward, M.B. (1999). Two-transitive actions on conjugacy Classes. Bulletin of the Australian Mathematical Society, 59: 409-420. doi: 10.1017/S0004972700033086
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Cambridge University Press
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