scholarly journals Residually finite tubular groups

2019 ◽  
Vol 150 (6) ◽  
pp. 2937-2951
Author(s):  
Nima Hoda ◽  
Daniel T. Wise ◽  
Daniel J. Woodhouse
Keyword(s):  
Finite Graph ◽  
Vertex Group ◽  
Residual Finiteness ◽  
Graph Of Groups ◽  
Residually Finite ◽  
Single Vertex

A tubular group G is a finite graph of groups with ℤ2 vertex groups and ℤ edge groups. We characterize residually finite tubular groups: G is residually finite if and only if its edge groups are separable. Methods are provided to determine if G is residually finite. When G has a single vertex group an algorithm is given to determine residual finiteness.

ON RESIDUAL FINITENESS OF GRAPHS OF NILPOTENT GROUPS

2004 ◽  
Vol 14 (04) ◽  
pp. 403-408
Author(s):  
E. RAPTIS ◽  
O. TALELLI ◽  
D. VARSOS
Keyword(s):  
Finite Groups ◽  
Finite Graph ◽  
Nilpotent Groups ◽  
Fundamental Groups ◽  
Residual Finiteness ◽  
Graph Of Groups ◽  
Residually Finite ◽  
Edge Group ◽  
Residually Finite Groups ◽  
Torsion Free

Here we characterize the residually finite groups G which are the fundamental groups of a finite graph of finitely generated torsion-free nilpotent groups. Namely we show that G is residually finite if and only if for each edge group of the graph of groups the two edge monomorphisms differ essentially by an isomorphism of certain subgroups of the Mal'cev completion of the corresponding vertex groups.

On the Residual Finiteness of Polygonal Products of Nilpotent Groups

1992 ◽  
Vol 35 (3) ◽  
pp. 390-399 ◽  
Author(s):  
Goansu Kim ◽  
C. Y. Tang
Keyword(s):  
Nilpotent Groups ◽  
Vertex Group ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Residually Finite ◽  
Cyclic Subgroups ◽  
Isolated Subgroup ◽  
Torsion Free

AbstractIn general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.

Residual finiteness of free products of combinatorial strict inverse semigroups

1994 ◽  
Vol 124 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Karl Auinger
Keyword(s):  
Inverse Semigroup ◽  
Free Product ◽  
Inverse Semigroups ◽  
Residual Finiteness ◽  
Free Products ◽  
Residually Finite

It is shown that the free product of two residually finite combinatorial strict inverse semigroups in general is not residually finite. In contrast, the free product of a residually finite combinatorial strict inverse semigroup and a semilattice is residually finite.

THE COMBINATION THEOREM AND QUASICONVEXITY

2001 ◽  
Vol 11 (02) ◽  
pp. 185-216 ◽  
Author(s):  
ILYA KAPOVICH
Keyword(s):  
Fundamental Group ◽  
Isometric Embedding ◽  
Normal Forms ◽  
Vertex Group ◽  
Graph Of Groups

We show that if G is a fundamental group of a finite k-acylindrical graph of groups where every vertex group is word-hyperbolic and where every edge-monomorphism is a quasi-isometric embedding, then all the vertex groups are quasiconvex in G (the group G is word-hyperbolic by the Combination Theorem of M. Bestvina and M. Feighn). This allows one, in particular, to approximate the word metric on G by normal forms for this graph of groups.

Residually finite groups of finite rank

1989 ◽  
Vol 106 (3) ◽  
pp. 385-388 ◽  
Author(s):  
Alexander Lubotzky ◽  
Avinoam Mann
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Finite Rank ◽  
Prime Order ◽  
Residual Finiteness ◽  
Infinite Groups ◽  
Finiteness Conditions ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Residually Finite Groups

The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters’, show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird. Thus it seems reasonable to impose the type of condition that enables us to apply the theory of finite groups. Two such conditions are local finiteness and residual finiteness, and here we are interested in the latter. Specifically, we consider residually finite groups of finite rank, where a group is said to have rank r, if all finitely generated subgroups of it can be generated by r elements. Recall that a group is said to be virtually of some property, if it has a subgroup of finite index with this property. We prove the following result:Theorem 1. A residually finite group of finite rank is virtually locally soluble.

Residual finiteness, subgroup separability and conjugacy separability of certain HNN extensions

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
K. Wong ◽  
P. Wong
Keyword(s):  
Finite Groups ◽  
Finite Subgroup ◽  
Residual Finiteness ◽  
Residually Finite ◽  
Hnn Extensions ◽  
Conjugacy Separability ◽  
Subgroup Separability ◽  
Conjugacy Separable

AbstractIn this note we shall give characterisations for HNN extensions of non-cyclic polycyclic-by-finite groups with normal infinite cyclic associated subgroups to be residually finite, subgroup separable and conjugacy separable.

Residual Finiteness of Commutative Rings and Schemes

1973 ◽  
Vol 25 (5) ◽  
pp. 960-972
Author(s):  
Aron Simis
Keyword(s):  
Commutative Rings ◽  
Residual Finiteness ◽  
Residually Finite ◽  
Definition Of

This work grew out of a preliminary announcement (Notices of the Amer. Math. Soc. 18 (1971)). Here we modify the definition of residual finiteness given in [2]. This allows us, first of all, to consider a broader class of rings which are “essentially” residually finite and, secondly, to extend the notion to schemes. We then show that, for various topologies on the category of schemes, our notion of residual finiteness is local so that all relevant questions appear already at the ring level.

scholarly journals Note on the residual finiteness of Artin groups

2018 ◽  
Vol 21 (3) ◽  
pp. 531-537 ◽  
Author(s):  
Rubén Blasco-García ◽  
Arye Juhász ◽  
Luis Paris
Keyword(s):  
Artin Group ◽  
Artin Groups ◽  
Residual Finiteness ◽  
Residually Finite ◽  
Coxeter Graph ◽  
Admissible Partition ◽  
Group A

Abstract Let A be an Artin group. A partition {\mathcal{P}} of the set of standard generators of A is called admissible if, for all {X,Y\in\mathcal{P}} , {X\neq Y} , there is at most one pair {(s,t)\in X\times Y} which has a relation. An admissible partition {\mathcal{P}} determines a quotient Coxeter graph {\Gamma/\mathcal{P}} . We prove that, if {\Gamma/\mathcal{P}} is either a forest or an even triangle free Coxeter graph and {A_{X}} is residually finite for all {X\in\mathcal{P}} , then A is residually finite.

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