Enumeration of Schur rings over small groups

Matan Ziv-Av

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations


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 languageEnglish
Title of host publicationComputer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783319105147
StatePublished - 1 Jan 2014
Event16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014 - Warsaw, Poland
Duration: 8 Sep 201412 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8660 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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