Results 1 to 10 of about 93 (67)
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
exaly +6 more sources
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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Every group is a maximal subgroup of a naturally occurring free idempotent generated semigroup [PDF]
Semigroup Forum, 2013 Gray and Ruskuc have shown that any group G occurs as the maximal subgroup of some free idempotent generated semigroup IG(E) on a biordered set of idempotents E, thus resolving a long standing open question. Given the group G, they make a careful choice for E and use a certain amount of well developed machinery.
Victoria Gould +2 more
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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, Dolinka Igor
exaly +4 more sources
On the syntactic monoids associated with a class of synchronized codes. [PDF]
ScientificWorldJournal, 2013 A complete code C over an alphabet A is called synchronized if there exist x, y ∈ C* such that xA*∩A*y⊆C*. In this paper we describe the syntactic monoid Syn(C+) of C+ for a complete synchronized code C over A such that C+, the semigroup generated by C, is a single class of its syntactic congruence PC+.
Wang SF.
europepmc +2 more sources
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 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
exaly +3 more sources
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
exaly +3 more sources
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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Free idempotent generated semigroups and endomorphism monoids of independence algebras [PDF]
Semigroup Forum, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang Dandan +2 more
exaly +5 more sources