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

Authors:
John L. Hayden and David L. Winter

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

MSC:
Primary 20D05

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

MathSciNet review:
0450393

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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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© Copyright 1977
American Mathematical Society