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Idempotent transformations of finite groups
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 233, no 1, 56-86 p.Article in journal (Refereed) Published
Abstract [en]

We describe the action of idempotent transformations on finite groups. We show that finiteness is preserved by such transformations and enumerate all possible values such transformations can assign to a fixed finite simple group. This is done in terms of the first two homology groups. We prove for example that except special linear groups, such an orbit can have at most 7 elements. We also study the action of monomials of idempotent transformations on finite groups and show for example that orbits of this action are always finite.

Place, publisher, year, edition, pages
2013. Vol. 233, no 1, 56-86 p.
Keyword [en]
Cellularization of groups, Simple groups
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-109596DOI: 10.1016/j.aim.2012.09.030ISI: 000311773000003Scopus ID: 2-s2.0-84867954617OAI: oai:DiVA.org:kth-109596DiVA: diva2:584385
Funder
Swedish Research Council, 2005-2008 2009-6102
Note

QC 20130109

Available from: 2013-01-09 Created: 2013-01-08 Last updated: 2017-12-06Bibliographically approved

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  • Other locale
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