Finite simple groups containing a self-centralizing element of order 6

Hayden, John L.; Winter, David L.

doi:10.1090/S0002-9939-1977-0450393-1

Finite simple groups containing a self-centralizing element of order $6$
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by John L. Hayden and David L. Winter

Proc. Amer. Math. Soc. 66 (1977), 202-204

DOI: https://doi.org/10.1090/S0002-9939-1977-0450393-1

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Abstract:

By a self-centralizing element of a group we mean an element which commutes only with its powers. In this paper we establish the following result: Theorem. Let G be a finite simple group which has a self-centralizing element of order 6. Assume that G has only one class of involutions. Then G is isomorphic to one of the groups ${M_{11}},{J_1},{L_3}(3),{L_2}(11),{L_2}(13)$.

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