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A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
Published/Copyright:
May 12, 2006
Abstract
We set up a Grothendieck spectral sequence which generalizes the Lyndon–Hochschild–Serre spectral sequence for a group extension K ↣ G ↠ Q by allowing the normal subgroup K to be replaced by a subgroup, or family of subgroups which satisfy a weaker condition than normality. This is applied to establish a decomposition theorem for certain groups as fundamental groups of graphs of Poincaré duality groups. We further illustrate the method by proving a cohomological vanishing theorem which applies for example to Thompson's group F.
Received: 2004-10-29
Accepted: 2005-02-15
Published Online: 2006-05-12
Published in Print: 2006-01-26
© Walter de Gruyter
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Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
