The Root-Class Residuality of the Fundamental Groups of Certain Graphs of Groups with Central Edge Subgroups

2021 ◽  
Vol 62 (6) ◽  
pp. 1119-1132
Author(s):  
E. V. Sokolov
Keyword(s):  
Fundamental Groups ◽  
Graphs Of Groups ◽  
Root Class

scholarly journals FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM

2005 ◽  
Vol 15 (01) ◽  
pp. 95-128 ◽  
Author(s):  
ILYA KAPOVICH ◽  
RICHARD WEIDMANN ◽  
ALEXEI MYASNIKOV
Keyword(s):  
Solvable Groups ◽  
Fundamental Groups ◽  
Membership Problem ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Uniform Subgroup ◽  
Right Angled Artin Groups ◽  
Subgroup Membership Problem

We introduce a combinatorial version of Stallings–Bestvina–Feighn–Dunwoody folding sequences. We then show how they are useful in analyzing the solvability of the uniform subgroup membership problem for fundamental groups of graphs of groups. Applications include coherent right-angled Artin groups and coherent solvable groups.

Weak potency of certain fundamental groups of graphs of groups

2017 ◽  
Author(s):  
Muhammad Sufi ◽  
Kok Bin Wong ◽  
Peng Choon Wong
Keyword(s):  
Fundamental Groups ◽  
Graphs Of Groups

scholarly journals $C^*$-algebras associated with the fundamental groups of graphs of groups

2005 ◽  
Vol 97 (1) ◽  
pp. 49 ◽  
Author(s):  
Rui Okayasu
Keyword(s):  
Fundamental Group ◽  
Hyperbolic Group ◽  
Fundamental Groups ◽  
Graph Of Groups ◽  
C Algebra ◽  
C Algebras ◽  
Graphs Of Groups ◽  
Word Hyperbolic Group ◽  
Dimensional Boundary ◽  
The Ideal

We construct a nuclear $C^*$-algebra associated with the fundamental group of a graph of groups of finite type. It is well-known that every word-hyperbolic group with zero-dimensional boundary, in other words, every group acting trees with finite stabilizers is given by the fundamental group of such a graph of groups. We show that our $C^*$-algebra is $*$-isomorphic to the crossed product arising from the associated boundary action and is also given by a Cuntz-Pimsner algebra. We also compute the K-groups and determine the ideal structures of our $C^*$-algebras.

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

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