Permutation groups and derangements of odd prime order

Tim Burness; Michael Giudici

doi:10.1016/j.jcta.2017.04.007

Permutation groups and derangements of odd prime order

Tim Burness
, Michael Giudici

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

361 Downloads (Pure)

Abstract

Let G be a transitive permutation group of degree n. We say that G is 2'-
elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 20-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.

Original language	English
Pages (from-to)	102-130
Number of pages	29
Journal	Journal of Combinatorial Theory, Series A
Volume	151
Early online date	5 May 2017
DOIs	https://doi.org/10.1016/j.jcta.2017.04.007
Publication status	Published - Oct 2017

Keywords

Derangement
Elusive group
Quasiprimitive group
Biquasiprimitive group
Arc-transitive graph

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10.1016/j.jcta.2017.04.007

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at http://www.sciencedirect.com/science/article/pii/S0097316517300456. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 358 KBLicence: CC BY-NC-ND

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title = "Permutation groups and derangements of odd prime order",

abstract = "Let G be a transitive permutation group of degree n. We say that G is 2'- elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 20-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.",

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T1 - Permutation groups and derangements of odd prime order

AU - Burness, Tim

AU - Giudici, Michael

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N2 - Let G be a transitive permutation group of degree n. We say that G is 2'- elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 20-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.

AB - Let G be a transitive permutation group of degree n. We say that G is 2'- elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 20-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.

KW - Derangement

KW - Elusive group

KW - Quasiprimitive group

KW - Biquasiprimitive group

KW - Arc-transitive graph

U2 - 10.1016/j.jcta.2017.04.007

DO - 10.1016/j.jcta.2017.04.007

M3 - Article (Academic Journal)

SN - 0097-3165

VL - 151

SP - 102

EP - 130

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

ER -

Permutation groups and derangements of odd prime order

Abstract

Keywords

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