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June 2012 Fusion systems on metacyclic 2-groups
Benjamin Sambale
Osaka J. Math. 49(2): 325-329 (June 2012).

Abstract

Let $P$ be a finite metacyclic $2$-group and $\mathcal{F}$ a fusion system on $P$. We prove that $\mathcal{F}$ is nilpotent unless $P$ has maximal class or $P$ is homocyclic, i.e. $P$ is a direct product of two isomorphic cyclic groups. As a consequence we obtain the numerical invariants for $2$-blocks with metacyclic defect groups. This paper is a part of the author's PhD thesis.

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Benjamin Sambale. "Fusion systems on metacyclic 2-groups." Osaka J. Math. 49 (2) 325 - 329, June 2012.

Information

Published: June 2012
First available in Project Euclid: 20 June 2012

zbMATH: 1247.20025
MathSciNet: MR2945751

Subjects:
Primary: 20D15
Secondary: 20C15 , 20C20

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 2 • June 2012
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