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Fusion Systems on Bicyclic 2-Groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  08 January 2016

Benjamin Sambale
Benjamin Sambale*
Affiliation:
Institut für Mathematik, Friedrich-Schiller-Universität, 07743 Jena, Germany
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Abstract

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We classify all (saturated) fusion systems on bicyclic 2-groups. Here, a bicyclic group is a product of two cyclic subgroups. This extends previous work on fusion systems on metacyclic 2-groups. As an application we prove Olsson's conjecture for all blocks with bicyclic defect groups.

Keywords

fusion systemsbicyclic 2-groupsOlsson's conjecture

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 4 , November 2016 , pp. 989 - 1018
Copyright
Copyright © Edinburgh Mathematical Society 2016