scholarly journals Amalgamated Free Products of Inverse Semigroups

1998 ◽  
Vol 208 (2) ◽  
pp. 399-424 ◽  
Author(s):  
J.B. Stephen
Keyword(s):  
Inverse Semigroups ◽  
Free Products ◽  
Amalgamated Free Products

scholarly journals ON THE GROWTH OF GROUPS AND AUTOMORPHISMS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 869-874 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Finitely Generated ◽  
Free Products ◽  
Dehn Functions ◽  
Amalgamated Free Products ◽  
Growth Functions ◽  
Growth Of Groups

We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.

scholarly journals Separating conjugates in amalgamated free products and HNN extensions

1980 ◽  
Vol 29 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Joan L. Dyer
Keyword(s):  
Nilpotent Groups ◽  
Conjugacy Classes ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Nontrivial Center ◽  
One Relator Groups ◽  
Amalgamated Subgroup ◽  
Conjugacy Separable ◽  
Base Group

AbstractA group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.

On Unital Full Amalgamated Free Products of Quasidiagonal C*-Algebras

2016 ◽  
Vol 50 (1) ◽  
pp. 39-47
Author(s):  
Qihui Li ◽  
Don Hadwin ◽  
Jiankui Li ◽  
Xiujuan Ma ◽  
Junhao Shen
Keyword(s):  
Free Products ◽  
C Algebras ◽  
Amalgamated Free Products

scholarly journals Stable commutator length in amalgamated free products

2015 ◽  
Vol 07 (04) ◽  
pp. 693-717 ◽  
Author(s):  
Tim Susse
Keyword(s):  
Geometric Model ◽  
Free Products ◽  
Cyclic Groups ◽  
Amalgamated Free Products ◽  
Torus Knot ◽  
Knot Complements ◽  
Stable Commutator Length ◽  
Free Abelian Groups ◽  
Commutator Length ◽  
Boundary Mapping

We show that stable commutator length is rational on free products of free abelian groups amalgamated over ℤk, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parametrize all surfaces with specified boundary mapping to this space. Using this work we provide a topological algorithm to compute stable commutator length in these groups. Further, we use the methods developed to show that in free products of cyclic groups the stable commutator length of a fixed word varies quasirationally in the orders of the free factors.

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.

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