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Solution of the problem of expressibility in amalgamated products of groups

✍ Scribed by I. V. Dobrynina

Publisher
Springer US
Year
2010
Tongue
English
Weight
127 KB
Volume
166
Category
Article
ISSN
1573-8795

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G and G amalgamating a common subgroup H. The first problem that 1 2 one encounters is that the residual finiteness of G and G does not imply 1 2 w x in general that G is residually finite. Baumslag 1 proved that if G and 1 G are either both free or both torsion-free finitely generated nilpotent 2 g

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For a class of extensions of free products of groups, a description is given of the space of the real-valued functions Ο• defined on the group G and satisfying the conditions (1) the set Ο• xy -Ο• x -Ο• y x y ∈ G is bounded; and (2) Ο• x n = nΟ• x for any x ∈ G and any n ∈ (the set of integers). Let G be