Results 1  10
of
38
Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems
, 2004
"... ..."
Tree Actions of Automorphism Groups
 J. Group Theory
"... We introduce conditions on a group action on a tree that are sufficient for the action to extend to the automorphism group. We apply this to two different classes of onerelator groups: certain BaumslagSolitar groups and onerelator groups with centre. In each case we derive results about the autom ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
(Show Context)
We introduce conditions on a group action on a tree that are sufficient for the action to extend to the automorphism group. We apply this to two different classes of onerelator groups: certain BaumslagSolitar groups and onerelator groups with centre. In each case we derive results about the automorphism group, and deduce that there are relatively few outer automorphisms.
On the automorphism group of generalized BaumslagSolitar groups
"... Abstract. A generalized BaumslagSolitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains nonabelian free groups or is virtually nilpotent of class ≤ 2. It has torsion only at finitely ma ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
(Show Context)
Abstract. A generalized BaumslagSolitar group (GBS group) is a finitely generated group G which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains nonabelian free groups or is virtually nilpotent of class ≤ 2. It has torsion only at finitely many primes. One may decide algorithmically whether Out(G) is virtually nilpotent or not. If it is, one may decide whether it is virtually abelian, or finitely generated. The isomorphism problem is solvable among GBS groups with Out(G) virtually nilpotent. If G is unimodular (virtually Fn × Z), then Out(G) is commensurable with a semidirect product Z k ⋊Out(H) with H virtually free. Contents
Some connections between residual finiteness, finite embeddability and the word problem
 Journal of London Mathematics Society
, 1969
"... ..."
(Show Context)
Splittings of generalized Baumslag–Solitar groups
, 2006
"... Abstract. We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually nonunique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (fully reduced decompositions) and ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually nonunique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (fully reduced decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the isomorphism problem for generalized Baumslag–Solitar groups with no nontrivial integral moduli.
TWISTED CONJUGACY CLASSES IN SYMPLECTIC GROUPS, MAPPING CLASS GROUPS AND BRAID GROUPS (INCLUDING AN APPENDIX WRITTEN WITH Francois Dahmani)
, 2007
"... We prove that the symplectic group Sp(2n, Z) and the mapping class group ModS of a compact surface S satisfy the R ∞ property. We also show that Bn(S), the full braid group on nstrings of a surface S, satisfies the R ∞ property in the cases where S is either the compact disk D, or the sphere S 2. ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We prove that the symplectic group Sp(2n, Z) and the mapping class group ModS of a compact surface S satisfy the R ∞ property. We also show that Bn(S), the full braid group on nstrings of a surface S, satisfies the R ∞ property in the cases where S is either the compact disk D, or the sphere S 2. This means that for any automorphism φ of G, where G is one of the above groups, the number of twisted φconjugacy classes is infinite.
Asymptotic cyclic expansion and bridge groups of formal proofs
 JOURNAL OF ALGEBRA
, 2001
"... Formal proofs, even simple ones, may hide an unexpected intricate combinatorics. We define a new combinatorial invariant, the bridge group of a proof, which encodes the cyclic structure of proofs in the sequent calculus. We compute the bridge groups of two infinite families of proofs and identify th ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Formal proofs, even simple ones, may hide an unexpected intricate combinatorics. We define a new combinatorial invariant, the bridge group of a proof, which encodes the cyclic structure of proofs in the sequent calculus. We compute the bridge groups of two infinite families of proofs and identify them with the Baumslag–Solitar and Gersten groups. We observe that the distortion of cyclic subgroups in these groups equals the asymptotic growth of the procedure of elimination of lemmas from the proofs.
Growth functions for some nonautomatic BaumslagSolitar groups
 Trans. Amer. Math. Soc
, 1994
"... Abstract. The growth function of a group is a generating function whose coefficients an are the number of elements in the group whose minimum length as a word in the generators is n. In this paper we use finite state automata to investigate the growth function for the BaumslagSolitar group of the f ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract. The growth function of a group is a generating function whose coefficients an are the number of elements in the group whose minimum length as a word in the generators is n. In this paper we use finite state automata to investigate the growth function for the BaumslagSolitar group of the form {a, b  a~lba = a2) based on an analysis of its combinatorial and geometric structure. In particular, we obtain a set of lengthminimal normal forms for the group which, although it does not form the language of a finite state automata, is nevertheless built up in a sufficiently coherent way that the growth function can be shown to be rational. The rationality of the growth function of this group is particularly interesting as it is known not to be synchronously automatic. The results in this paper generalize to the groups (a, b \ a~lba = am) for all positive integers m. 1.
Poisson Boundary of Discrete Groups
"... this paper. If there exists a Gequivariant map S assigning to pairs of distinct points (fl \Gamma ; fl + ) from @G nonempty subsets ("strips") S(fl \Gamma ; fl + ) ae G such that for any distinct fl 0 ; fl 1 ; fl 2 2 @G there are neighbourhoods O o ae G and O 1 ; O 2 ae @G with S(fl \Gam ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
this paper. If there exists a Gequivariant map S assigning to pairs of distinct points (fl \Gamma ; fl + ) from @G nonempty subsets ("strips") S(fl \Gamma ; fl + ) ae G such that for any distinct fl 0 ; fl 1 ; fl 2 2 @G there are neighbourhoods O o ae G and O 1 ; O 2 ae @G with S(fl \Gamma ; fl + ) " O o = ? for all points fl \Gamma 2 O 1 ; g+ 2 O 2 then the action of G on @G is mean proximal (Theorem 2.1.4)