Ends and amalgamated free products of groups

1972 ◽  
Vol 127 (3) ◽  
pp. 265-272 ◽  
Author(s):  
Peter C. Oxley
Keyword(s):  
Free Products ◽  
Amalgamated Free Products ◽  
Products Of Groups

scholarly journals Groups whose three-generator subgroups are free

1989 ◽  
Vol 40 (2) ◽  
pp. 163-174 ◽  
Author(s):  
Gilbert Baumslag ◽  
Peter B. Shalen
Keyword(s):  
Free Groups ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Products Of Groups

We define a certain class of groups, Ck, which we show to contain the class of all k-free groups. Our main theorem shows that certain amalgamated free products of groups in C3, are again in C3. In the appendix we show that many 3-manifold groups belong to Ck for suitable k.

Second Order Dehn Functions for Amalgamated Free Products of Groups

2009 ◽  
Vol 16 (04) ◽  
pp. 699-708
Author(s):  
Xiaofeng Wang ◽  
Xiaomin Bao
Keyword(s):  
Free Product ◽  
Upper Bound ◽  
Second Order ◽  
Free Products ◽  
Dehn Functions ◽  
Amalgamated Free Products ◽  
Products Of Groups ◽  
Amalgamated Free Product ◽  
Finite Set

A finite set of generators for a free product of two groups of type F3with a subgroup amalgamated, and an estimation for the upper bound of the second order Dehn functions of the amalgamated free product are carried out.

Units in Group Rings of Free Products of Prime Cyclic Groups

1998 ◽  
Vol 50 (2) ◽  
pp. 312-322 ◽  
Author(s):  
Michael A. Dokuchaev ◽  
Maria Lucia Sobral Singer
Keyword(s):  
Unit Group ◽  
Group Rings ◽  
Rational Group ◽  
Free Products ◽  
Structural Result ◽  
Cyclic Groups ◽  
Amalgamated Free Products ◽  
Products Of Groups ◽  
Finite Subgroups ◽  
Zassenhaus Conjecture

AbstractLet G be a free product of cyclic groups of prime order. The structure of the unit group U(ℚG) of the rational group ring ℚG is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of U(ℚG), up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in ℤ G is proved. A strong version of the Tits Alternative for U(ℚG) is obtained as a corollary of the structural result.

scholarly journals Free product decompositions in images of certain free products of groups

2007 ◽  
Vol 310 (1) ◽  
pp. 57-69
Author(s):  
N.S. Romanovskii ◽  
John S. Wilson
Keyword(s):  
Free Product ◽  
Free Products ◽  
Products Of Groups

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.

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