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Computing normalizers of permutation groups efficiently using isomorphisms of association schemes

Author:

Izumi MiyamotoAuthors Info & Claims

ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation

Pages 220 - 224

https://doi.org/10.1145/345542.345637

Published: 01 July 2000 Publication History

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Abstract

This note presents an algorithm to speed up the computation of normalizers of permutation groups. It is an application of computation of isomorphisms of association schemes.

References

[1]

E. Bannai and T. Ito. Algebraic Combinatorics I: Association Schemes. Benjamin/Cummings, Menlo Park, CA, 1984.

Google Scholar

[2]

The GAP Group. GAP- Croups, Algorithms and Programming, Version ~. Lehrstuhl D f Mathematik, Rheinisch WestfSlische Technisch Hochschule, Aachen, Germany and School of Mathematical and Computational Sciences, U. St.Andrews Scotland, 1997.

Google Scholar

[3]

A. Hanaki. Data of association schemes, published at WWW. http://math.shinshu-u.ac.jp/-hanaki, 1999.

Google Scholar

[4]

A. Hanaki and I. Miyamoto. Classification of association schemes with 16 and 17 vertices. Kyushu J. Math., 52:383-395, 1998.

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Google Scholar

[5]

A. Hanaki and I. Miyamoto. Classification of association schemes with 18 and 19 vertices. Korean J. Comp. App. Math., 5:543-551, 1998.

Google Scholar

[6]

A. Hulpke. Konstruktion transitiver Permutationsgruppen. Dissertation, RWTH-Aachen, 1996.

Google Scholar

[7]

B. Mckay. Practical graph isomorphism. In Proceedings of the Tenth Manitoba Conference on Numerical Mathematics and Computing, Vol. 1(Winnipeg, Man., 1930), pages 45-87. Congressus Numerantium 30, 1981.

Google Scholar

[8]

H. Theiflen. Eine Methode zur Normalisatorberechnung in Permutationsgruppen mit Anwendungen in der Konstruktion primitiver Gruppen. Dissertation, RWTH-Aachen, 1997.

Google Scholar

Cited By

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Miyamoto I(2019)A combinatorial approach to doubly transitive permutation groupsDiscrete Mathematics10.1016/j.disc.2007.08.032308:14(3073-3081)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.disc.2007.08.032
Miyamoto I(2010)An improvement of a function computing normalizers for permutation groupsProceedings of the Third international congress conference on Mathematical software10.5555/1888390.1888407(62-68)Online publication date: 13-Sep-2010
https://dl.acm.org/doi/10.5555/1888390.1888407
Miyamoto I(2010)An Improvement of a Function Computing Normalizers for Permutation GroupsMathematical Software – ICMS 201010.1007/978-3-642-15582-6_13(62-68)Online publication date: 2010
https://doi.org/10.1007/978-3-642-15582-6_13
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Index Terms

Computing normalizers of permutation groups efficiently using isomorphisms of association schemes
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms
2. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory

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This paper describes algorithms for constructing a Hall @p-subgroup H of a finite soluble group G and the normaliser N"G(H). If G has composition length n, then H and N"G(H) can be constructed using O(n^4 log |G|) and O(n^5 log |G|) group ...

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Published In

ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation

July 2000

309 pages

ISBN:1581132182

DOI:10.1145/345542

Editor:
Carlo Traverso
Univ. di Pisa

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 2000

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Miyamoto I(2019)A combinatorial approach to doubly transitive permutation groupsDiscrete Mathematics10.1016/j.disc.2007.08.032308:14(3073-3081)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.disc.2007.08.032
Miyamoto I(2010)An improvement of a function computing normalizers for permutation groupsProceedings of the Third international congress conference on Mathematical software10.5555/1888390.1888407(62-68)Online publication date: 13-Sep-2010
https://dl.acm.org/doi/10.5555/1888390.1888407
Miyamoto I(2010)An Improvement of a Function Computing Normalizers for Permutation GroupsMathematical Software – ICMS 201010.1007/978-3-642-15582-6_13(62-68)Online publication date: 2010
https://doi.org/10.1007/978-3-642-15582-6_13
Miyamoto IWang D(2007)A computation of some multiply homogeneous superschemes from transitive permutation groupsProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277588(293-298)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277588
Miyamoto ITrager B(2006)An improvement of GAP normalizer function for permutation groupsProceedings of the 2006 international symposium on Symbolic and algebraic computation10.1145/1145768.1145808(234-238)Online publication date: 9-Jul-2006
https://dl.acm.org/doi/10.1145/1145768.1145808

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Association schemes and permutation groups

Isomorphisms of groups related to flocks

Constructing normalisers in finite soluble groups

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Association schemes and permutation groups

Isomorphisms of groups related to flocks

Constructing normalisers in finite soluble groups

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