On minimal faithful permutation representations of finite groups

L. G. Kovács; Cheryl E. Praeger

doi:10.1017/s0004972700018797

On minimal faithful permutation representations of finite groups

L. G. Kovács^*
, Cheryl E. Praeger

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

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 S_n. 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.

Original language	English
Pages (from-to)	311-317
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	62
Issue number	2
DOIs	https://doi.org/10.1017/s0004972700018797
Publication status	Published - Oct 2000

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abstract = "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.",

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AU - Praeger, Cheryl E.

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N2 - 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.

AB - 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.

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DO - 10.1017/s0004972700018797

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EP - 317

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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ER -

On minimal faithful permutation representations of finite groups

Abstract

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