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Centralizers involving Mathieu groups

Published online by Cambridge University Press:  17 April 2009

M.J. Curran
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand.
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Abstract

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A simple group G cannot contain a central involution t with CG(t) = 〈t〉 × M, where M is isomorphic to a simple Mathieu group.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Curran, M.J., “Groups with decomposable involution centralizers”, submitted.Google Scholar
[2]Glauberman, George, “Central elements in core-free groups”, J. Algebra 4 (1966), 403420.CrossRefGoogle Scholar
[3]Held, Dieter, “The simple groups related to M 24”, J. Algebra 13 (1969), 253296.CrossRefGoogle Scholar
[4]Janko, Zvonimir, “A new finite simple group with abelian Sylow 2-subgroups and its characterization”, J. Algebra 3 (1966), 147186.CrossRefGoogle Scholar
[5]Janko, Zvonimir and Thompson, John G., “On a class of finite simple groups of Ree”, J. Algebra 4 (1966), 274292.CrossRefGoogle Scholar
[6]Wong, W.J., “A characterization of the Mathieu group M 12”, Math. Z. 84 (1964), 378388.CrossRefGoogle Scholar