Idempotent transformations of finite groups
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
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.
Cellularization of groups, Simple groups
IdentifiersURN: urn:nbn:se:kth:diva-109596DOI: 10.1016/j.aim.2012.09.030ISI: 000311773000003ScopusID: 2-s2.0-84867954617OAI: oai:DiVA.org:kth-109596DiVA: diva2:584385
FunderSwedish Research Council, 2005-2008 2009-6102
QC 201301092013-01-092013-01-082013-01-09Bibliographically approved