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On minimal faithful permutation representations of finite groups

Published online by Cambridge University Press:  17 April 2009

David Easdown  and
Cheryl E. Praeger
David Easdown
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia
Cheryl E. Praeger
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia
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Abstract

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The minimal (faithful) degree μ(G) of a finite group G is the least positive integer n such that G ≲ Sn. Clearly if H ≤ G then μ(H) ≤ μ(G). However if N ◃ G then it is possible for μ(G/N) to be greater than μ(G); such groups G are here called exceptional. Properties of exceptional groups are investigated and several families of exceptional groups are given. For example it is shown that the smallest exceptional groups have order 32.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 2 , October 1988 , pp. 207 - 220
Copyright
Copyright © Australian Mathematical Society 1988

References

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