Triangles of Groups

Chermak, Andrew

doi:10.2307/2155050

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1995

2015

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Cited by 2 publications

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“…A similar result holds for non-spherical Corson diagrams, see [13]. While these two results can be proved by nice arguments based on Euler's formula for planar graphs, spherical Corson diagrams are much harder to investigate, see, for example, [2,12].…”

Section: Introductionmentioning

confidence: 82%

The Tits alternative for non-spherical triangles of groups

Cuno

Lehnert

2015

Trans. London Math. Soc.

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Triangles of groups have been introduced by Gersten and Stallings. They are, roughly speaking, a generalization of the amalgamated free product of two groups and occur in the framework of Corson diagrams. First, we prove an intersection theorem for Corson diagrams. Then, we focus on triangles of groups. It has been shown by Howie and Kopteva that the colimit of a hyperbolic triangle of groups contains a non-abelian free subgroup. We give two natural conditions, each of which ensures that the colimit of a non-spherical triangle of groups either contains a non-abelian free subgroup or is virtually solvable.

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Section: Introductionmentioning

confidence: 82%