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

R Gray; Nik Ruskuc

doi:10.1112/plms/pdr054

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

Research output: Contribution to journal › Article › peer-review

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 ∈ E be an arbitrary idempotent satisfying |im (e)| = r ≤ n − 2. We prove that the maximal subgroup of the free idempotent generated semigroup over E containing e is isomorphic to the symmetric group S_r.

Original language	English
Pages (from-to)	997-1018
Number of pages	28
Journal	Proceedings of the London Mathematical Society
Volume	104
Issue number	5
Early online date	24 Jan 2012
DOIs	https://doi.org/10.1112/plms/pdr054
Publication status	Published - May 2012

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Theory of Semigroups: Representation theory of Semigroups
Ruskuc, N. (PI)
EPSRC
1/04/12 → 30/09/15
Project: Standard
Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. (PI)
EPSRC
1/02/08 → 31/01/11
Project: Standard

Cite this

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

Abstract

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Projects

Theory of Semigroups: Representation theory of Semigroups

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids

Cite this