Some new examples of simple $p$-local compact groups

González, Alex; Lozano, Toni; Ruiz, Albert

doi:10.48550/arxiv.1512.00284

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2017

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“…In either case, if F is simple, then the action of the Weyl group Aut F (S 0 ) on the If F ∼ = F S (X) for some p-compact group X with S ∈ Syl p (X), then X is connected by [GLR,Proposition 4.9(a)]. Then X is a central product of connected, simple p-compact groups, and hence is simple if F is simple.…”

Section: Introductionmentioning

confidence: 99%

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Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: III

Oliver¹,

Ruiz²

2017

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We finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian p-groups with an abelian subgroup of index p. In particular, this gives many new examples illustrating the enormous variety of exotic examples that can arise. In addition, we classify all simple fusion systems over infinite nonabelian discrete p-toral groups with an abelian subgroup of index p. In all of these cases (finite or infinite), we reduce the problem to one of listing all F p G-modules (for G finite) satisfying certain conditions: a problem which was solved in the earlier paper [CrOS] using the classification of finite simple groups.

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Section: Introductionmentioning

confidence: 99%

“…When F is a saturated fusion system over an infinite discrete p-toral group S, there are well defined normal subsystems O p (F ) (see [Gon, Appendix B]), and O p ′ (F ) (see [GLR,), with the same properties as in the finite case. So we could define reduced fusion systems in this context just as in the finite case.…”

Section: Introductionmentioning

confidence: 99%