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STRICT INEQUALITIES FOR MINIMAL DEGREES OF DIRECT PRODUCTS

Part of: Permutation groups

Published online by Cambridge University Press:  10 March 2009

NEIL SAUNDERS
NEIL SAUNDERS*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia (email: [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 non-negative integer n such that G embeds in the symmetric group Sym(n). Work of Johnson and Wright in the 1970s established conditions for when μ(H×K)=μ(H)+μ(K), for finite groups H and K. Wright asked whether this is true for all finite groups. A counter-example of degree 15 was provided by the referee and was added as an addendum in Wright’s paper. Here we provide two counter-examples; one of degree 12 and the other of degree 10.

Keywords

faithful permutation representationscomplex reflection groupsmonomial reflection groups

MSC classification

Secondary: 20B35: Subgroups of symmetric groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 23 - 30
Copyright
Copyright © Australian Mathematical Society 2009

References

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