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104
PROFINITE TOPOLOGICAL SPACES
"... Abstract. It is well known [Hoc69, Joy71] that profinite T0spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space.(2) The T0reflection of (X,τ) i ..."
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Abstract. It is well known [Hoc69, Joy71] that profinite T0spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space.(2) The T0reflection of (X
On the profinite topology of rightangled Artin groups
 J.of Algebra
"... Abstract. In the present work, we give necessary and sufficient conditions on the graph of a rightangled Artin group that determine whether the group is subgroup separable or not. Also we show that rightangled Artin groups are residually torsionfree nilpotent. Moreover, we investigate the profini ..."
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Cited by 9 (0 self)
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the profinite topology of F2 × F2 and of the group L in [18], which are the only obstructions for the subgroup separability of the rightangled Artin groups. We show that the profinite topology of the above groups is strongly connected with the profinite topology of F2. 1.
CLOSURES OF REGULAR LANGUAGES FOR PROFINITE TOPOLOGIES
"... Abstract. The PinReutenauer algorithm gives a method, that can be viewed as a descriptive procedure, to compute the closure in the free group of a regular language with respect to the Hall topology. A similar descriptive procedure is shown to hold for the pseudovariety A of aperiodic semigroups, w ..."
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Abstract. The PinReutenauer algorithm gives a method, that can be viewed as a descriptive procedure, to compute the closure in the free group of a regular language with respect to the Hall topology. A similar descriptive procedure is shown to hold for the pseudovariety A of aperiodic semigroups
ON GROUPS WHOSE SUBGROUPS ARE CLOSED IN THE PROFINITE TOPOLOGY
"... Abstract. A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERFproperty is studied for nilpotent groups, soluble groups, locally finite groups and FCgroups. A complete characterization is given of FCgroups which are ERF. 2000 Mathematics ..."
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Abstract. A group is called extended residually finite (ERF) if every subgroup is closed in the profinite topology. The ERFproperty is studied for nilpotent groups, soluble groups, locally finite groups and FCgroups. A complete characterization is given of FCgroups which are ERF. 2000
Extending partial automorphisms and the profinite topology on free groups
 Tran. AMS
, 2000
"... Abstract. A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C1 and C2 are structures in C, C1 finite, C1 ⊆ C2, and p1,p2,...,pn are partial automorphisms of C1 extending to automorphisms of C2, then there exist a finite structure C3 in C and ..."
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and automorphisms α1,α2,...,αn of C3 extending the pi. We will prove that some classes of structures have the EPPA and show the equivalence of these kinds of results with problems related with the profinite topology on free groups. In particular, we will give a generalisation of the theorem, due to Ribes
Sofic groups and profinite topology on free groups
, 2009
"... We give a definition of weakly sofic groups (wsofic groups). Our definition is rather natural extension of the definition of sofic groups where instead of Hamming metric on symmetric groups we use general biinvariant metrics on finite groups. The existence of non wsofic groups is equivalent to so ..."
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Cited by 8 (1 self)
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to some conjecture about profinite topology on free groups.
Inverse Automata And Profinite Topologies On A Free Group
 J. Pure and Applied Algebra
, 1999
"... This paper gives an elementary, selfcontained proof that a finite product of finitely generated subgroups of a free group is closed in the profinite topology. The proof uses inverse automata (immersions) and inverse monoid theory. Generalizations are given to other topologies. In particular, we obt ..."
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Cited by 7 (3 self)
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This paper gives an elementary, selfcontained proof that a finite product of finitely generated subgroups of a free group is closed in the profinite topology. The proof uses inverse automata (immersions) and inverse monoid theory. Generalizations are given to other topologies. In particular, we
Monoid Kernels And Profinite Topologies On The Free Abelian Group
 Bull. Austral. Math. Soc
, 1999
"... . To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a profinite topology on any finite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can effectively compute ..."
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Cited by 4 (2 self)
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. To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a profinite topology on any finite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can effectively
Free Product, Profinite Topology and Finitely Generated Subgroups.
"... We consider the following property for a group G : (RZn ) if H1 ; : : : ; Hn are finitely generated subgroups of G then the set H1H2 \Delta \Delta \Delta Hn = fh1 \Delta \Delta \Delta hn jh1 2 H1 ; : : : ; hn 2 Hng is closed with respect to the profinite topology of G. It is obvious that finite gro ..."
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We consider the following property for a group G : (RZn ) if H1 ; : : : ; Hn are finitely generated subgroups of G then the set H1H2 \Delta \Delta \Delta Hn = fh1 \Delta \Delta \Delta hn jh1 2 H1 ; : : : ; hn 2 Hng is closed with respect to the profinite topology of G. It is obvious that finite
Results 1  10
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104