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Profinite Categories and Semidirect Products
"... After developing a theory of implicit operations and proving an analogue of Reiterman's theorem for categories, this paper addresses two complementary questions for semidirect products and twosided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity is vali ..."
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Cited by 37 (18 self)
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After developing a theory of implicit operations and proving an analogue of Reiterman's theorem for categories, this paper addresses two complementary questions for semidirect products and twosided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity
Profinite groups, profinite completions and a conjecture of Moore
"... Let R be any ring (with 1), Γ a group and RΓ the corresponding group ring. Let H be a subgroup of Γ of finite index. Let M be an RΓ−module, whose restriction to RH is projective. Moore’s conjecture [5]: Assume for every nontrivial element x in Γ, at least one of the following two conditions holds: M ..."
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Cited by 2 (2 self)
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’s theorem on cohomological dimension of profinite groups. Supported by the Fund for the Promotion of Research at the Technion.
Abstract commensurators of profinite groups
"... Abstract. In this paper we initiate a systematic study of the abstract commensurators of profinite groups. The abstract commensurator of a profinite group G is a group Comm(G) which depends only on the commensurability class of G. We study various properties of Comm(G); in particular, we find two na ..."
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Cited by 15 (0 self)
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of the Grigorchuk group as an open subgroup. On the other hand, we show that some profinite groups cannot be embedded as open subgroups of compactly generated topologically simple groups. Several celebrated rigidity theorems, like Pink’s analogue of Mostow’s strong rigidity theorem for simple algebraic groups
Profinite Homotopy Theory
 DOCUMENTA MATH.
, 2008
"... We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and prospaces. One motivation is the étale homotopy theory of schemes in which higher profinite étale homotopy g ..."
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Cited by 6 (3 self)
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We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and prospaces. One motivation is the étale homotopy theory of schemes in which higher profinite étale homotopy
Universal Profinite Domains
 Information and Computation
, 1987
"... . We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite dom ..."
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Cited by 17 (1 self)
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domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators. As a special instance of this construction, a universal domain for the category SFP is demonstrated. Necessary conditions for the existence of solutions for domain
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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Cited by 20 (2 self)
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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.
Modular Representations Of Profinite Groups∗
, 2009
"... Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a profinite group G, where k is a finite field of characterist ..."
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Cited by 1 (1 self)
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finitely generated k[[G]]modules and show that the expected conjugacy properties hold for sources this requires additional assumptions. Finally we prove a direct analogue of Green’s Indecomposability Theorem for finitely generated modules over a virtually prop group 2
Profinite properties of graph manifolds
, 2009
"... Let M be a closed, orientable, irreducible, geometrizable 3manifold. We prove that the profinite topology on the fundamental group of π1(M) is efficient with respect to the JSJ decomposition of M. We go on to prove that π1(M) is good, in the sense of Serre, if all the pieces of the JSJ decompositio ..."
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Cited by 8 (3 self)
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decomposition are. We also prove that if M is a graph manifold then π1(M) is conjugacy separable. A group G is conjugacy separable if every conjugacy class is closed in the profinite topology on G. This can be thought of as a strengthening of residual finiteness (which is equivalent to the trivial subgroup’s
PROFINITE METHODS IN AUTOMATA THEORY
"... Abstract. This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory. ..."
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Abstract. This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory.
PROFINITE METHODS IN AUTOMATA THEORY
"... Abstract. This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory. In mathematics, padic analysis is a powerfu ..."
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Abstract. This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory. In mathematics, padic analysis is a
Results 1  10
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