Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 24 Jan 2012Embargo end date: 01 Jan 2011 United Kingdom English Publisher:WileyJournal:Proceedings of the London Mathematical Society, volume 104, pages 997-1,018 (issn: 0024-6115,

Copyright policy )Funded by:FCT | Semigroups and Languages

Authors: Gray, R.; Ruskuc, N.;

doi: 10.1112/plms/pdr054 , 10.48550/arxiv.1101.1833

arXiv: 1101.1833

handle: 10023/2134

Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

- Summary
- Subjects
- Metrics

Abstract

Let T_n be the full transformation semigroup of all mappings from the set {1,...,n} to itself under composition. Let E = E(T_n) denote the set of idempotents of T_n and let e be an arbitrary idempotent satisfying |im(e)|=r < n-1. We prove that the maximal subgroup of the free idempotent generated semigroup over E containing e is isomorphic to the symmetric group S_r.

28 pages

Country

United Kingdom

Related Organizations

University of East Anglia
United Kingdom
University of St Andrews
United Kingdom
University of Lisbon
Portugal

Keywords

FOS: Mathematics, QA Mathematics, Group Theory (math.GR), 20M05, 05E15, 20F05, QA, Mathematics - Group Theory, 510, 620

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	25
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%