Enumeration of Schur rings over the group A5

Mikhail Klin; Matan Ziv-Av

doi:10.1007/978-3-319-02297-0_19

Enumeration of Schur rings over the group A₅

Mikhail Klin, Matan Ziv-Av

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

With the aid of the computer algebra system GAP (together with the extension package COCO-II) all S-rings over the smallest non-abelian simple group A₅ of order 60 are enumerated. It turns out that there are 2848 S-rings over A₅, in 163 orbits under the action of S₅. Among them there are 505 non-Schurian S-rings, in 19 orbits. We discuss the entire picture of this rich computer data and try to present an initial outline of a human explanation for most of the results obtained.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing - 15th International Workshop, CASC 2013, Proceedings
Pages	219-230
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-319-02297-0_19
State	Published - 10 Oct 2013
Event	15th International Workshop on Computer Algebra in Scientific Computing, CASC 2013 - Berlin, Germany Duration: 9 Sep 2013 → 13 Sep 2013

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8136 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th International Workshop on Computer Algebra in Scientific Computing, CASC 2013
Country/Territory	Germany
City	Berlin
Period	9/09/13 → 13/09/13

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-02297-0_19

Cite this

Klin, M., & Ziv-Av, M. (2013). Enumeration of Schur rings over the group A₅. In Computer Algebra in Scientific Computing - 15th International Workshop, CASC 2013, Proceedings (pp. 219-230). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8136 LNCS). https://doi.org/10.1007/978-3-319-02297-0_19

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Klin, M & Ziv-Av, M 2013, Enumeration of Schur rings over the group A₅. in Computer Algebra in Scientific Computing - 15th International Workshop, CASC 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8136 LNCS, pp. 219-230, 15th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, Berlin, Germany, 9/09/13. https://doi.org/10.1007/978-3-319-02297-0_19

Enumeration of Schur rings over the group A₅. / Klin, Mikhail; Ziv-Av, Matan.
Computer Algebra in Scientific Computing - 15th International Workshop, CASC 2013, Proceedings. 2013. p. 219-230 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8136 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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