Results 1 to 10 of about 5,622,676 (84)
On maximal subgroups of free idempotent generated semigroups [PDF]
Israel Journal of Mathematics, 2011 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.
Nik Ruškuc
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Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid [PDF]
Proceedings of the London Mathematical Society, 2012 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 ...
Gray, R., Ruskuc, N.
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Subgroups of free idempotent generated semigroups need not be free [PDF]
Journal of Algebra, 2009 We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free abelian group of rank 2. This is the first example of a non-free subgroup of a free idempotent generated semigroup.
Stuart W Margolis +2 more
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A note on maximal subgroups of free idempotent generated semigroups over bands [PDF]
Periodica Mathematica Hungarica, 2012 We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands.
Igor Dolinka
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The free idempotent generated locally inverse semigroup [PDF]
Semigroup Forum, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luis Oliveira
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A Note on Free Idempotent Generated Semigroups over the Full Monoid of Partial Transformations [PDF]
Communications in Algebra, 2013 Recently, Gray and Ruskuc (arXiv:1101.1833) proved that if e is a rank k idempotent transformation of the set {1,...,n} to itself and k<=n-2, then the maximal subgroup of the free idempotent generated semigroup over the full transformation monoid T_n containing e is isomorphic to the symmetric group S_k.
Igor Dolinka
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Subgroups of free idempotent generated regular semigroups
Semigroup Forum, 1980 In [6] it is shown that the maximal subgroups of the free idempotent generated regular semigroup which is determined by the biordered set of a completely O-simple semigroup are free. In this note we shall extend this result to a wider class of semigroups.
K S S Nambooripad
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Free idempotent generated semigroups and endomorphism monoids of independence algebras [PDF]
Semigroup Forum, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victoria Gould
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Semigroup Forum, 2022 With each semigroup one can associate a partial algebra, called the biordered set, which captures important algebraic and geometric features of the structure of idempotents of that semigroup. For a biordered set $\mathcal{E}$, one can construct the free idempotent-generated semigroup over $\mathcal{E}$, $\mathsf{IG}(\mathcal{E})$, which is the free-est
Igor Dolinka
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Free idempotent generated semigroups and endomorphism monoids of free G-acts
Journal of Algebra, 2015 The study of the free idempotent generated semigroup $\mathrm{IG}(E)$ over a biordered set $E$ began with the seminal work of Nambooripad in the 1970s and has seen a recent revival with a number of new approaches, both geometric and combinatorial. Here we study $\mathrm{IG}(E)$ in the case $E$ is the biordered set of a wreath product $G\wr \mathcal{T ...
Victoria Gould, Igor Dolinka
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