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Finite Simple Groups Containing a Self-Centralizing Element of Order 6

John L. Hayden and David L. Winter
Proceedings of the American Mathematical Society
Vol. 66, No. 2 (Oct., 1977), pp. 202-204
DOI: 10.2307/2040929
Stable URL: http://www.jstor.org/stable/2040929
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Finite Simple Groups Containing a Self-Centralizing Element of Order 6
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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 $M_{11}, J_1, L_3(11), L_2(13)$.

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