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ON THE DIMENSION OF GROUPS THAT SATISFY CERTAIN CONDITIONS ON THEIR FINITE SUBGROUPS

Part of: Low-dimensional topology Connections with homological algebra and category theory

Published online by Cambridge University Press:  04 November 2020

LUIS JORGE SÁNCHEZ SALDAÑA
LUIS JORGE SÁNCHEZ SALDAÑA*
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Cd. Universitaria, Colonia Copilco el Bajo, Delegación Coyoacán, Mexico City04510, Mexico, e-mail: luisjorge@ciencias.unam.mx
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Abstract

We say a group G satisfies properties (M) and (NM) if every nontrivial finite subgroup of G is contained in a unique maximal finite subgroup, and every nontrivial finite maximal subgroup is self-normalizing. We prove that the Bredon cohomological dimension and the virtual cohomological dimension coincide for groups that admit a cocompact model for EG and satisfy properties (M) and (NM). Among the examples of groups satisfying these hypothesis are cocompact and arithmetic Fuchsian groups, one-relator groups, the Hilbert modular group, and 3-manifold groups.

MSC classification

Primary: 20J05: Homological methods in group theory
Secondary: 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 45 - 50
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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