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Abstract
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free
regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister–Schreier type rewriting.
regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister–Schreier type rewriting.
Original language | English |
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Pages (from-to) | 147-176 |
Journal | Israel Journal of Mathematics |
Volume | 189 |
Issue number | 1 |
Early online date | 9 Sept 2011 |
DOIs | |
Publication status | Published - 2012 |
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Dive into the research topics of 'On maximal subgroups of free idempotent generated semigroups'. Together they form a unique fingerprint.Projects
- 4 Finished
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Theory of Semigroups: Representation theory of Semigroups
Ruskuc, N. (PI)
1/04/12 → 30/09/15
Project: Standard
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Automata Languages Decidability: Automata, Languages, Decidability in Algebra
Ruskuc, N. (PI) & Quick, M. (CoI)
1/03/10 → 31/05/14
Project: Standard
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Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D. (PI)
1/02/08 → 31/01/11
Project: Standard