An estimate for the rank of the intersection of subgroups in free amalgamated products of two groups with normal finite amalgamated subgroup

2013 ◽  
Vol 204 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Alexander O Zakharov
Keyword(s):  
Intersection Of Subgroups ◽  
Amalgamated Products ◽  
Amalgamated Subgroup

scholarly journals On Permutational Products of Groups:Part 2-amalgamated products

1971 ◽  
Vol 12 (1) ◽  
pp. 21-34
Author(s):  
R. J. Gregorac
Keyword(s):  
Free Product ◽  
Group Structure ◽  
Exact Nature ◽  
Free Products ◽  
Products Of Groups ◽  
Generalized Free Product ◽  
Amalgamated Products ◽  
Amalgamated Subgroup ◽  
Apparent Similarity ◽  
The Relationship

The standard methods of constructing generalized free products of groups (with a single amalgamated subgroup) and permutational products of groups are to consider groups of permutations on sets. Although there is an apparent similarity between these two constructions, the exact nature of the relationship is not clear. The following addendum to [4] grew out of an attempt to determine this relationship. By noting that the original construction of permutational products (B. H. Neumann [7]) deals with a group of permutations on a group (although the group structure has been previously ignored; see [7], [8]) we here give an extension of the original permutational product-construction which yields both the generalized free product and the permutational products as groups of permutations on groups. A generalized free product is represented as a group of permutations on the ordinary free product of the constituents of the underlying group amalgam and a permutational product is a group of permutations on the direct product of the constituents of the amalgam.

The Free Product of Two Groups with a Malnormal Amalgamated Subgroup

1971 ◽  
Vol 23 (5) ◽  
pp. 933-959 ◽  
Author(s):  
A. Karrass ◽  
D. Solitar
Keyword(s):  
Free Product ◽  
Defining Relation ◽  
Amalgamated Products ◽  
Amalgamated Subgroup ◽  
Image Position

In [1], B. Baumslag defined a subgroup U of a group G to be malnormal in G if gug–1 ∈ U, 1 ≠ u ∈ U, implies that g ∈ U. Baumslag considered the class of amalgamated products (A * B; U) in which U is malnormal in both A and B. These amalgamated products play an important role in the investigations of B. B. Newman [13] of groups with one defining relation having torsion. In this paper, we shall be concerned primarily with a generalization of this class.Let U be a subgroup of a group G and let u ∈ U. Then the extended normalizer EG(u, U) of u relative to U in G is defined byif u ≠ 1, and by EG(u, U) = U if u = 1.

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.

scholarly journals A Magnus theorem for some amalgamated products

2019 ◽  
Vol 47 (12) ◽  
pp. 5348-5360
Author(s):  
Carsten Feldkamp
Keyword(s):  
Amalgamated Products

Examples of amalgamated products

2001 ◽  
Vol 124 (1) ◽  
pp. 279-284
Author(s):  
Inna Bumagina
Keyword(s):  
Amalgamated Products

scholarly journals On bounded cohomology of amalgamated products of groups

2004 ◽  
Vol 2004 (40) ◽  
pp. 2103-2121 ◽  
Author(s):  
Igor V. Erovenko
Keyword(s):  
Cohomology Group ◽  
Initial Segment ◽  
Singular Part ◽  
Bounded Cohomology ◽  
Products Of Groups ◽  
Amalgamated Products ◽  
Cohomology Sequence

We investigate the structure of the singular part of the second bounded cohomology group of amalgamated products of groups by constructing an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.

Semistability of amalgamated products and HNN-extensions

1992 ◽  
Vol 98 (471) ◽  
pp. 0-0 ◽  
Author(s):  
Michael L. Mihalik ◽  
Steven T. Tschantz
Keyword(s):  
Hnn Extensions ◽  
Amalgamated Products
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