Enumeration of Schur rings over small groups

Matan Ziv-Av

doi:10.1007/978-3-319-10515-4_35

Enumeration of Schur rings over small groups

Matan Ziv-Av

Department of Mathematics

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

12 Scopus citations

Abstract

By optimizing the algorithms used in COCO and COCO-II, we enumerated all Schur rings over the groups of orders up to 63. A few statistical views of results with respect to Schur property, amount and type of generators and primitivity are presented. Discussion of the details of the old algorithms and the improvements we implemented in order to achieve those results is included. We compare the results to similar computerized efforts (Hanaki and Miyamoto, Pech and Reichard, Heinze), as well as to theoretical classifications of Schur groups. The computer based results may assist the theoretical efforts to classify all Schur groups, over abelian and non-abelian groups.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings
Publisher	Springer Verlag
Pages	491-500
Number of pages	10
ISBN (Print)	9783319105147
DOIs	https://doi.org/10.1007/978-3-319-10515-4_35
State	Published - 1 Jan 2014
Event	16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014 - Warsaw, Poland Duration: 8 Sep 2014 → 12 Sep 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8660 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014
Country/Territory	Poland
City	Warsaw
Period	8/09/14 → 12/09/14

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-10515-4_35

Cite this

Ziv-Av, M. (2014). Enumeration of Schur rings over small groups. In Computer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings (pp. 491-500). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8660 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-10515-4_35

@inproceedings{735bb7e8530241e896d38adf1cb23067,

title = "Enumeration of Schur rings over small groups",

abstract = "By optimizing the algorithms used in COCO and COCO-II, we enumerated all Schur rings over the groups of orders up to 63. A few statistical views of results with respect to Schur property, amount and type of generators and primitivity are presented. Discussion of the details of the old algorithms and the improvements we implemented in order to achieve those results is included. We compare the results to similar computerized efforts (Hanaki and Miyamoto, Pech and Reichard, Heinze), as well as to theoretical classifications of Schur groups. The computer based results may assist the theoretical efforts to classify all Schur groups, over abelian and non-abelian groups.",

author = "Matan Ziv-Av",

year = "2014",

month = jan,

day = "1",

doi = "10.1007/978-3-319-10515-4\_35",

language = "English",

isbn = "9783319105147",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "491--500",

booktitle = "Computer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings",

address = "Germany",

note = "16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014 ; Conference date: 08-09-2014 Through 12-09-2014",

}

Ziv-Av, M 2014, Enumeration of Schur rings over small groups. in Computer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8660 LNCS, Springer Verlag, pp. 491-500, 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014, Warsaw, Poland, 8/09/14. https://doi.org/10.1007/978-3-319-10515-4_35

Enumeration of Schur rings over small groups. / Ziv-Av, Matan.
Computer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings. Springer Verlag, 2014. p. 491-500 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8660 LNCS).

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

TY - GEN

T1 - Enumeration of Schur rings over small groups

AU - Ziv-Av, Matan

PY - 2014/1/1

Y1 - 2014/1/1

N2 - By optimizing the algorithms used in COCO and COCO-II, we enumerated all Schur rings over the groups of orders up to 63. A few statistical views of results with respect to Schur property, amount and type of generators and primitivity are presented. Discussion of the details of the old algorithms and the improvements we implemented in order to achieve those results is included. We compare the results to similar computerized efforts (Hanaki and Miyamoto, Pech and Reichard, Heinze), as well as to theoretical classifications of Schur groups. The computer based results may assist the theoretical efforts to classify all Schur groups, over abelian and non-abelian groups.

AB - By optimizing the algorithms used in COCO and COCO-II, we enumerated all Schur rings over the groups of orders up to 63. A few statistical views of results with respect to Schur property, amount and type of generators and primitivity are presented. Discussion of the details of the old algorithms and the improvements we implemented in order to achieve those results is included. We compare the results to similar computerized efforts (Hanaki and Miyamoto, Pech and Reichard, Heinze), as well as to theoretical classifications of Schur groups. The computer based results may assist the theoretical efforts to classify all Schur groups, over abelian and non-abelian groups.

UR - https://www.scopus.com/pages/publications/84906972164

U2 - 10.1007/978-3-319-10515-4_35

DO - 10.1007/978-3-319-10515-4_35

M3 - Conference contribution

AN - SCOPUS:84906972164

SN - 9783319105147

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 491

EP - 500

BT - Computer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings

PB - Springer Verlag

T2 - 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014

Y2 - 8 September 2014 through 12 September 2014

ER -

Enumeration of Schur rings over small groups

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this