scholarly journals C*-algebras associated with amalgamated products of groups

1987 ◽  
Vol 29 (2) ◽  
pp. 143-148
Author(s):  
Bola O. Balogun
Keyword(s):  
Free Product ◽  
Discrete Groups ◽  
Verbal Subgroup ◽  
C Algebras ◽  
Products Of Groups ◽  
Amalgamated Products

Let V denote the class of discrete groups G which satisfy the following conditions (a), (b) and (c):(a) G = (A * B; K = φ(H)) is the free product of two groups A and B with the subgroup H amalgamated.(b) H does not contain the verbal subgroup A(X2) of A and K does not contain the verbal subgroup B(X2)of B.

scholarly journals A problem of expressibility in some amalgamated products of groups

2001 ◽  
Vol 71 (1) ◽  
pp. 105-115 ◽  
Author(s):  
Valerii Faiziev
Keyword(s):  
Free Group ◽  
Finite Subset ◽  
Proper Subgroup ◽  
Arbitrary Group ◽  
Double Cosets ◽  
Verbal Subgroup ◽  
Products Of Groups ◽  
Countable Rank ◽  
Amalgamated Products

AbstractLet S be a subset of a group G such that S−1 = S. Denote by gr (S) the subgroup of G generated by S, and by ls(g) the length of an element g ∈ gr(S) relative to the set S. Suppose that V is a finite subset of a free group F of countable rank such that the verbal subgroup V (F) is a proper subgroup of F. For an arbitrary group G, denote by (G) the set of values in G of all the words from the set V. In the present paper, for amalgamated products G = A *HB such that A ≠ H and the number of double cosets of B by H is at least three, the infiniteness of the set {ls(g) | g ∈ gr(S)}, where S = (G) ∪ (G)−1, is estabilished.

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.

Simplicity Of Reduced Amalgamated Products of C*-Algebras

1994 ◽  
Vol 46 (4) ◽  
pp. 793-807 ◽  
Author(s):  
Kevin McClanahan
Keyword(s):  
Free Product ◽  
Sufficient Conditions ◽  
Minimal Projection ◽  
C Algebras ◽  
Amalgamated Products

AbstractWe give sufficient conditions for the simplicity of reduced amalgamated products of C*-algebras. We show that in some situations a minimal projection in a unital C*-algebra A is minimal in a free product A *-cB. We show that in certain situations if a minimal projection in A were minimal in a particular reduced free product of A and B then the reduced free product would be a simple C*-algebra which has finite and infinite projections.

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 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.

scholarly journals A five lemma for free products of groups with amalgamations

1970 ◽  
Vol 3 (1) ◽  
pp. 85-96 ◽  
Author(s):  
J. L. Dyer
Keyword(s):  
Free Product ◽  
Free Products ◽  
Products Of Groups ◽  
Five Lemma

This paper explores a five-lemma situation in the context of a free product of a family of groups with amalgamated subgroups (that is, a colimit of an appropriate diagram in the category of groups). In particular, for two families {Aα}, {Bα} of groups with amalgamated subgroups {Aαβ}, {Bαβ} and free products A, B we assume the existence of homomorphisms Aα → Bα whose restrictions Aαβ → Bαβ are isomorphisms and which induce an isomorphism A → B between the products. We show that the usual five-lemma conclusion is false, in that the morphisms Aα → Bα are in general neither monic nor epic. However, if all Bα → B are monic, Aα → Bα is always epic; and if Aα → A is monic, for all α, then Aα → Bα is an isomorphism.

scholarly journals Induced Coactions of Discrete Groups on C*-Algebras

1999 ◽  
Vol 51 (4) ◽  
pp. 745-770 ◽  
Author(s):  
Siegfried Echterhoff ◽  
John Quigg
Keyword(s):  
Quotient Group ◽  
Discrete Group ◽  
Discrete Groups ◽  
Crossed Products ◽  
C Algebras ◽  
Morita Equivalent ◽  
Close Relationship

AbstractUsing the close relationship between coactions of discrete groups and Fell bundles, we introduce a procedure for inducing a C*-coaction δ: D → D ⊗C*(G/N) of a quotient group G/N of a discrete group G to a C*-coaction Ind δ: Ind D → D ⊗C*(G) of G. We show that induced coactions behave in many respects similarly to induced actions. In particular, as an analogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D ×IndδG and D ×δG/N are always Morita equivalent. We also obtain nonabelian analogues of a theorem of Olesen and Pedersen which show that there is a duality between induced coactions and twisted actions in the sense of Green. We further investigate amenability of Fell bundles corresponding to induced coactions.

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