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83
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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being closed). Hempel [9] proved that the fundamental group of any geometrizable 3manifold is residually finite. In this paper, we investigate which 3manifolds have conjugacy separable fundamental group. 1 We also study Serre’s notion of goodness, another property related to the profinite topology
Cohomological properties of the profinite . . .
, 2007
"... We prove that the Bianchi groups, that is the groups PSL(2, O) where O is the ring of integers in an imaginary quadratic number field, are good. This is a property introduced by J.P. Serre which relates the cohomology groups of a group to those of its profinite completion. We also develop properties ..."
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We prove that the Bianchi groups, that is the groups PSL(2, O) where O is the ring of integers in an imaginary quadratic number field, are good. This is a property introduced by J.P. Serre which relates the cohomology groups of a group to those of its profinite completion. We also develop
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 13 (0 self)
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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
The triviality problem for profinite completions
, 2013
"... Abstract. We prove that there is no algorithm that can determine whether or not a finitely presented group has a nontrivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, nonpositively curved square complexes. We deduce that many other properties of gr ..."
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Cited by 3 (2 self)
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Abstract. We prove that there is no algorithm that can determine whether or not a finitely presented group has a nontrivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, nonpositively curved square complexes. We deduce that many other properties
Equational theories of profinite structures
, 2011
"... Things that I show are nothing remarkably new. This is rather a point of view than a new piece of theory. Profinite structures Add virtual objects to our world to make it more complete (e.g. compact). Equational theories What properties of languages can be expressed by (some) equations? Micha l Skrz ..."
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Cited by 1 (1 self)
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Things that I show are nothing remarkably new. This is rather a point of view than a new piece of theory. Profinite structures Add virtual objects to our world to make it more complete (e.g. compact). Equational theories What properties of languages can be expressed by (some) equations? Micha l
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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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
COCYCLE SUPERRIGIDITY FOR PROFINITE ACTIONS OF PROPERTY (T) GROUPS
, 2008
"... Consider a free ergodic measure preserving profinite action Γ � X (i.e. an inverse limit of actions Γ � Xn, with Xn finite) of a countable property (T) group Γ (more generally of a group Γ which admits an infinite normal subgroup Γ0 such that the inclusion Γ0 ⊂ Γ has relative property (T) and Γ/Γ0 i ..."
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Cited by 28 (3 self)
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Consider a free ergodic measure preserving profinite action Γ � X (i.e. an inverse limit of actions Γ � Xn, with Xn finite) of a countable property (T) group Γ (more generally of a group Γ which admits an infinite normal subgroup Γ0 such that the inclusion Γ0 ⊂ Γ has relative property (T) and Γ/Γ0
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.
Results 1  10
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