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A note on centralizers of involutions involving simple groups

Published online by Cambridge University Press:  17 April 2009

Donald Wright
Donald Wright
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria.
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Abstract

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If a finite group G has a ‘central’ involution t whose centralizer in G is (t) × H then, under certain conditions on H, G cannot be simple.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 425 - 426
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Curran, M.J., “Centralizers involving Mathieu groups”, Bull. Austral. Math. Soc. 13 (1975), 321–323.CrossRefGoogle Scholar
[2]Glauberman, George, “Central elements in core-free groups”, J. Algebra 4 (1966), 403–420.CrossRefGoogle Scholar
[3]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar