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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0450393-1
PII: S 0002-9939(1977)0450393-1
Article copyright: © Copyright 1977 American Mathematical Society