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The Σ2-invariants for graph products of indicable groups

✍ Scribed by John Meier; Holger Meinert; Leonard VanWyk

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
498 KB
Volume
99
Category
Article
ISSN
0166-8641

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✦ Synopsis

Given a finite simplicial graph G and groups G v for each vertex v ∈ G, the graph product GG is the free product of the vertex groups modulo the normal closure of all commutator groups [G v , G w ] where v and w are adjacent vertices. If all vertex groups are indicable we give a complete description of the homotopical invariant Σ 2 (GG) which captures, among other things, information determinining which normal subgroups above the commutator are finitely presented. In case some vertex group is not indicable, our result still gives an almost complete picture of Σ 2 (GG).

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