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Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

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Cai Heng LiAuthors Info & Claims

Journal of Algebraic Combinatorics: An International Journal, Volume 21, Issue 2

Pages 131 - 136

https://doi.org/10.1007/s10801-005-6903-3

Published: 01 March 2005 Publication History

Abstract

A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970's. It is shown that a connected arc transitive circulant of order n is one of the following: a complete graph K _n, a lexicographic product $\Sigma [{\bar K}_b]$ , a deleted lexicographic product $\Sigma [{\bar K}_b] - b\Sigma$ , where is a smaller arc transitive circulant, or is a normal circulant, that is, Auta has a normal cyclic regular subgroup. The description of this class of permutation groups is also used to describe the class of rotary Cayley maps in subsequent work.

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Cited By

Jin WTan L(2022)On diameter two Cayley graphsApplied Mathematics and Computation10.1016/j.amc.2022.127437434:COnline publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1016/j.amc.2022.127437
Chen JJin WLi C(2019)On 2-distance-transitive circulantsJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-018-0825-349:2(179-191)Online publication date: 15-Mar-2019
https://dl.acm.org/doi/10.1007/s10801-018-0825-3
Koike HKovács IMarušiă? DMuzychuk M(2019)Cyclic groups are CI-groups for balanced configurationsDesigns, Codes and Cryptography10.1007/s10623-018-0517-y87:6(1227-1235)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s10623-018-0517-y
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Index Terms

Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Permutations and combinations
    2. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image Journal of Algebraic Combinatorics: An International Journal

Journal of Algebraic Combinatorics: An International Journal Volume 21, Issue 2

March 2005

112 pages

ISSN:0925-9899

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Copyright © Copyright © 2005 Springer Science + Business Media, Inc.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 March 2005

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Cited By

Jin WTan L(2022)On diameter two Cayley graphsApplied Mathematics and Computation10.1016/j.amc.2022.127437434:COnline publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1016/j.amc.2022.127437
Chen JJin WLi C(2019)On 2-distance-transitive circulantsJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-018-0825-349:2(179-191)Online publication date: 15-Mar-2019
https://dl.acm.org/doi/10.1007/s10801-018-0825-3
Koike HKovács IMarušiă? DMuzychuk M(2019)Cyclic groups are CI-groups for balanced configurationsDesigns, Codes and Cryptography10.1007/s10623-018-0517-y87:6(1227-1235)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s10623-018-0517-y
Doyle JTucker TWatkins M(2018)Graphical Frobenius representationsJournal of Algebraic Combinatorics: An International Journal10.5555/3288648.328872248:3(405-428)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288648.3288722
Doyle JTucker TWatkins M(2018)Graphical Frobenius representationsJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-018-0814-648:3(405-428)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s10801-018-0814-6
Araújo JBentz WDobson EKonieczny JMorris J(2018)Automorphism Groups of Circulant Digraphs With Applications to Semigroup TheoryCombinatorica10.1007/s00493-016-3403-038:1(1-28)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1007/s00493-016-3403-0
Dobson ESpiga PVerret G(2016)Cayley graphs on abelian groupsCombinatorica10.1007/s00493-015-3136-536:4(371-393)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1007/s00493-015-3136-5
Jin WLiu WWang C(2016)Finite 2-Geodesic Transitive Abelian Cayley GraphsGraphs and Combinatorics10.1007/s00373-015-1601-y32:2(713-720)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1007/s00373-015-1601-y
Zhou JFeng Y(2014)Cubic bi-Cayley graphs over abelian groupsEuropean Journal of Combinatorics10.1016/j.ejc.2013.10.00536(679-693)Online publication date: 1-Feb-2014
https://dl.acm.org/doi/10.1016/j.ejc.2013.10.005
Li CLu ZPan J(2014)Finite vertex-primitive edge-transitive metacirculantsJournal of Algebraic Combinatorics: An International Journal10.1007/s10801-014-0507-840:3(785-804)Online publication date: 1-Nov-2014
https://dl.acm.org/doi/10.1007/s10801-014-0507-8
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