Skip to content

Research at St Andrews

On the Gruenberg–Kegel graph of integral group rings of finite groups

Research output: Contribution to journalArticle

Abstract

The prime graph question asks whether the Gruenberg–Kegel graph of an integral group ring ℤG, i.e. the prime graph of the normalized unit group of ℤG, coincides with that one of the group G. In this note, we prove for finite groups G a reduction of the prime graph question to almost simple groups. We apply this reduction to finite groups G whose order is divisible by at most three primes and show that the Gruenberg–Kegel graph of such groups coincides with the prime graph of G.
Close

Details

Original languageEnglish
Pages (from-to)619-631
Number of pages13
JournalInternational Journal of Algebra and Computation
Volume27
Issue number06
DOIs
StatePublished - 24 Aug 2017

    Research areas

  • Integral group rings, Torsion units, Gruenberg–Kegel graph

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. How to learn GAP - an open source software system for discrete computational mathematics

    Konovalov, A. & Torpey, M. C. Jan 2019

    Research output: Contribution to conferencePoster

  2. On skew braces and their ideals

    Konovalov, A., Smoktunowicz, A. & Vendramin, L. 22 Dec 2018 In : Experimental Mathematics. Latest Articles, 10 p.

    Research output: Contribution to journalArticle

  3. LAGUNA - Lie AlGebras and UNits of group Algebras, Version 3.9.1 (Refereed GAP package)

    Bovdi, V., Konovalov, A., Rossmanith, R. & Schneider, C. 30 Nov 2018

    Research output: Non-textual formSoftware

  4. Wedderga - Wedderburn Decomposition of Group Algebras, Version 4.9.5 (Refereed GAP package)

    Bakshi , G. K., Cristo , O. B., Herman, A., Konovalov, A., Maheshwary, S., Olivieri, A., Olteanu, G., del Río , Á. & Van Gelder, I. 30 Nov 2018

    Research output: Non-textual formSoftware

  5. Software Carpentry: Programming with GAP: Version 2.0

    Software Carpentry team 13 Nov 2018 Zenodo

    Research output: Other contribution

Related by journal

  1. A dynamical definition of f.g. virtually free groups

    Bennett, D. & Bleak, C. Feb 2016 In : International Journal of Algebra and Computation. 26, 1, p. 105-121 17 p.

    Research output: Contribution to journalArticle

  2. Every group is a maximal subgroup of the free idempotent generated semigroup over a band

    Dolinka, I. & Ruskuc, N. May 2013 In : International Journal of Algebra and Computation. 23, 3, p. 573-581

    Research output: Contribution to journalArticle

  3. Unary FA-presentable semigroups

    Cain, A. J., Ruskuc, N. & Thomas, R. M. 8 Jun 2012 In : International Journal of Algebra and Computation. 22, 4, 29 p., 1250038

    Research output: Contribution to journalArticle

  4. A SVARC-MILNOR LEMMA FOR MONOIDS ACTING BY ISOMETRIC EMBEDDINGS

    Gray, R. & Kambites, M. Nov 2011 In : International Journal of Algebra and Computation. 21, 7, p. 1135-1147 13 p.

    Research output: Contribution to journalArticle

ID: 250971182