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On exotic saturated fusion systems. (English) Zbl 1338.20013

Summary: In this paper, we prove that a product \(\mathcal F_1\times\mathcal F_2\) of saturated fusion systems is exotic if and only if at least one of the factors is exotic. This result provides a method to construct new exotic fusion systems by known exotic fusion systems. We also investigate central products of saturated fusion systems.

MSC:

20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
55R35 Classifying spaces of groups and \(H\)-spaces in algebraic topology
20D15 Finite nilpotent groups, \(p\)-groups
20D40 Products of subgroups of abstract finite groups
20C20 Modular representations and characters
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