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Finite soluble groups have large centralisers

Published online by Cambridge University Press:  17 April 2009

John Cossey
John Cossey
Affiliation:
Department of Mathematics, Faculty of Science, The Australian National University, G.P.O. Box 4, Canberra, 2601, Australian Capital Territory, Australia.
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Abstract

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We say that a finite group G has a large centraliser if G contains a non-central element x with |CG (x)| > |G|½. We prove that every finite soluble group has a large centraliser, confirming a conjecture of Bertram and Herzog.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 2 , April 1987 , pp. 291 - 298
Copyright
Copyright © Australian Mathematical Society 1987

References

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