On fixed points of elements in primitive permutation groups

Martin W. Liebeck; Aner Shalev

doi:10.1016/j.jalgebra.2014.08.038

On fixed points of elements in primitive permutation groups

Martin W. Liebeck^*, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

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

7 Scopus citations

Abstract

The fixity of a finite permutation group is the maximal number of fixed points of a non-identity element. We study the fixity of primitive groups of degree n, showing that apart from a short list of exceptions, the fixity of such groups is at least n^1/6. We also prove that there is usually an involution fixing at least n^1/6 points.

Original language	American English
Pages (from-to)	438-459
Number of pages	22
Journal	Journal of Algebra
Volume	421
DOIs	https://doi.org/10.1016/j.jalgebra.2014.08.038
State	Published - 1 Jan 2015

Bibliographical note

Funding Information:
The authors are grateful for the support of an EPSRC grant EP/H018891/1 . The second author acknowledges the support of grants from the Israel Science Foundation ( 2008194 ) and ERC ( 247034 ).

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Fixed points
Fixity
Involution fixity
Involutions
Permutation groups
Primitive permutation groups

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10.1016/j.jalgebra.2014.08.038

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abstract = "The fixity of a finite permutation group is the maximal number of fixed points of a non-identity element. We study the fixity of primitive groups of degree n, showing that apart from a short list of exceptions, the fixity of such groups is at least n1/6. We also prove that there is usually an involution fixing at least n1/6 points.",

keywords = "Fixed points, Fixity, Involution fixity, Involutions, Permutation groups, Primitive permutation groups",

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N2 - The fixity of a finite permutation group is the maximal number of fixed points of a non-identity element. We study the fixity of primitive groups of degree n, showing that apart from a short list of exceptions, the fixity of such groups is at least n1/6. We also prove that there is usually an involution fixing at least n1/6 points.

AB - The fixity of a finite permutation group is the maximal number of fixed points of a non-identity element. We study the fixity of primitive groups of degree n, showing that apart from a short list of exceptions, the fixity of such groups is at least n1/6. We also prove that there is usually an involution fixing at least n1/6 points.

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KW - Fixity

KW - Involution fixity

KW - Involutions

KW - Permutation groups

KW - Primitive permutation groups

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VL - 421

SP - 438

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

On fixed points of elements in primitive permutation groups

Abstract

Bibliographical note

Keywords

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