Results 41 to 50 of about 77 (63)
Finitely Generated Idempotent-free Semilattice-Indecomposable Semigroups with Relations I (Algebraic Semigroups, Formal Languages and Computation)openaire
Subgroups of free idempotent generated semigroups need not be free
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.
Mark Brittenham +2 more
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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 ...
Yang Dandan +2 more
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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, Ruškuc N
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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 +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, Dolinka Igor
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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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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 ...
Nik Ruškuc
exaly +5 more sources