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Profinite Methods in Semigroup Theory
 Int. J. Algebra Comput
, 2000
"... this paper. The extended bibliography given below shows other important contributions by Azevedo, Costa, Delgado, Pin, Teixeira, Volkov, Weil and Zeitoun. ..."
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this paper. The extended bibliography given below shows other important contributions by Azevedo, Costa, Delgado, Pin, Teixeira, Volkov, Weil and Zeitoun.
Profinite Methods in Finite Semigroup Theory
, 2001
"... This paper is a survey of the authors' recent results in the theory of finite semigroups using profinite techniques. This involves the study of free profinite semigroups, whose structure encodes algebraic and combinatorial properties of finite semigroups. ..."
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Cited by 5 (4 self)
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This paper is a survey of the authors' recent results in the theory of finite semigroups using profinite techniques. This involves the study of free profinite semigroups, whose structure encodes algebraic and combinatorial properties of finite semigroups.
Profinite groups associated with weakly primitive substitutions, Fundam
 Prikl. Mat
, 2007
"... Abstract. A uniformly recurrent pseudoword is an element of a free profinite semigroup in which every finite factor appears in every sufficiently long finite factor. An alternative characterization is as a pseudoword which is a factor of all its infinite factors, that is one which lies ..."
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Abstract. A uniformly recurrent pseudoword is an element of a free profinite semigroup in which every finite factor appears in every sufficiently long finite factor. An alternative characterization is as a pseudoword which is a factor of all its infinite factors, that is one which lies
A WREATH PRODUCT APPROACH TO CLASSICAL SUBGROUP THEOREMS
, 812
"... Abstract. We provide elementary proofs of the NielsenSchreier Theorem and the Kurosh Subgroup Theorem via wreath products. Our and profinite categories. A new proof that open subgroups of quasifree profinite groups are quasifree is also given. 1. ..."
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Abstract. We provide elementary proofs of the NielsenSchreier Theorem and the Kurosh Subgroup Theorem via wreath products. Our and profinite categories. A new proof that open subgroups of quasifree profinite groups are quasifree is also given. 1.
Solvable monoids with commuting idempotents
"... The notion of Abelian kernel of a finite monoid extends the notion of derived subgroup of a finite group. In this line, an extension of the notion of solvable group to monoids is quite natural: they are the monoids such that the chain of Abelian kernels ends with the submonoid generated by the idemp ..."
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The notion of Abelian kernel of a finite monoid extends the notion of derived subgroup of a finite group. In this line, an extension of the notion of solvable group to monoids is quite natural: they are the monoids such that the chain of Abelian kernels ends with the submonoid generated by the idempotents. We prove in this paper that the nite idempotent commuting monoids satisfying this property are precisely those whose subgroups are solvable.
PRESENTATIONS OF SCHÜTZENBERGER GROUPS OF MINIMAL SUBSHIFTS
"... Abstract. In previous work, the first author established a natural bijection between minimal subshifts and maximal regularJclasses of free profinite semigroups. In this paper, the Schützenberger groups of such Jclasses are investigated in particular in respect to a conjecture proposed by the first ..."
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Abstract. In previous work, the first author established a natural bijection between minimal subshifts and maximal regularJclasses of free profinite semigroups. In this paper, the Schützenberger groups of such Jclasses are investigated in particular in respect to a conjecture proposed by the first author concerning their profinite presentation. The conjecture is established for several types of minimal subshifts associated with substitutions. The Schützenberger subgroup of the Jclass corresponding to the ProuhetThueMorse subshift is shown to admit a somewhat simpler presentation, from which it follows that it satisfies the conjecture, that it has rank three, and that it is nonfree relatively to any pseudovariety of groups. 1.
A GEOMETRIC INTERPRETATION OF THE SCHÜTZENBERGER GROUP OF A MINIMAL SUBSHIFT
, 2015
"... The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geome ..."
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The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthe ́ et. al.
Profinite Identities for Finite Semigroups Whose Subgroups Belong to a Given Pseudovariety
"... We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite proidentity basis for the pseudovariety H of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of ..."
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We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite proidentity basis for the pseudovariety H of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of finite groups.
ON THE IRREDUCIBILITY OF PSEUDOVARIETIES OF SEMIGROUPS
"... Abstract. We show that, for every pseudovariety of groups H, the pseudovariety ¯ H, consisting of all finite semigroups all of whose subgroups lie in H, is irreducible for join and the Mal’cev and semidirect products. The proof involves a Rees matrix construction which motivates the study of iterate ..."
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Abstract. We show that, for every pseudovariety of groups H, the pseudovariety ¯ H, consisting of all finite semigroups all of whose subgroups lie in H, is irreducible for join and the Mal’cev and semidirect products. The proof involves a Rees matrix construction which motivates the study of iterated Mal’cev products with the pseudovariety of bands. We further provide a strict infinite filtration for ¯ H using such iterated Mal’cev products, in which the decidability of each level depends only on the decidability of H. 1.