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On minimal faithful permutation representations of finite groups

Published online by Cambridge University Press:  17 April 2009

L. G. Kovács  and
Cheryl E. Praeger
L. G. Kovács
Affiliation:
Australian National University, Canberra ACT 0200, Australia e-mail: [email protected]
Cheryl E. Praeger
Affiliation:
University of Western Australia, Perth WA 6907, Australia e-mail: [email protected]
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Abstract

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The minimal faithful permutation degree μ(G) of a finite group G is the least positive integer n such that G is isomorphic to a subgroup of the symmetric group Sn. Let N be a normal subgroup of a finite group G. We prove that μ(G/N) ≤ μ(G) if G/N has no nontrivial Abelian normal subgroup. There is an as yet unproved conjecture that the same conclusion holds if G/N is Abelian. We investigate the structure of a (hypothetical) minimal counterexample to this conjecture.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 311 - 317
Copyright
Copyright © Australian Mathematical Society 2000

References

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