Products in fusion systems

Henke, Ellen

doi:10.1016/j.jalgebra.2012.11.037

Cited by 15 publications

(20 citation statements)

References 10 publications

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“…We will use that there is a notion of a product EX. Such a product was first introduced by Aschbacher [Asc11, Chapter 8] with a simplified construction given in [Hen13]. We argue here based on the latter construction.…”

Section: K-normalizers Of P-subgroups In Normal Subsystemsmentioning

confidence: 95%

Normalizers and centralizers of $p$-subgroups in normal subsystems of fusion systems

Henke¹

2021

Preprint

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Section: K-normalizers Of P-subgroups In Normal Subsystemsmentioning

confidence: 95%

Normalizers and centralizers of $p$-subgroups in normal subsystems of fusion systems

Henke¹

2021

Preprint

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“…This is the unique saturated subsystem D of F over T R with O p (D) = O p (E). See [Asc11, Chapter 8] or [Hen13] for a concrete description.…”

Section: Proof It Follows From Lemma 42 That (I) Implies (Ii) Asmentioning

confidence: 99%

“…by a finite group of characteristic p. Furthermore, if F is constrained and G is a model for F, then every normal subsystem of F is realized by a normal subgroup of G. We also use that, for every saturated fusion system F over S, every normal subsystem E of F and every subgroup R of S, there is a product subsystem ER defined (cf. [Asc11, Chapter 8] or [Hen13]).…”

Section: Introductionmentioning

confidence: 99%

Kernels of Localities

Grazian¹,

Henke²

2021

Preprint

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“…We use in an essential way following theorem of Aschbacher, which allows one to consider the (internal) product of a p-group with a normal subsystem. See also [25] for a simplification of Aschbacher's construction and proof of saturation.…”

Section: Proposition 12 An Automorphism Of a Direct Product Of Indeco...mentioning

confidence: 99%

A characterization of the 2-fusion system of L4(q)

Lynd

2015

Journal of Algebra

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We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F = O 2 (F ), O 2 (F ) = 1, and the centralizer of the component is a cyclic 2-group, it is shown that F is uniquely determined as the 2-fusion system of L 4 (q 1 ) for some q 1 ≡ 3 (mod 4). This should be viewed as a contribution to a program recently outlined by M. Aschbacher for the classification of simple fusion systems at the prime 2. The corresponding problem in the component-type portion of the classification of finite simple groups (the L 2 (q), A 7 standard form problem) was one of the last to be completed, and was ultimately only resolved in an inductive context with heavy artillery. Thanks primarily to requiring the component to be Baumann, our main arguments by contrast require only 2-fusion analysis and transfer. We deduce a companion result in the category of groups.

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Products in fusion systems

Abstract: We revisit the notion of a product of a normal subsystem with a p-subgroup as defined by Aschbacher [Asc11, Chapter 8]. In particular, we give a previously unknown, more transparent construction.

Cited by 15 publications

References 10 publications

Normalizers and centralizers of $p$-subgroups in normal subsystems of fusion systems

Normalizers and centralizers of $p$-subgroups in normal subsystems of fusion systems

Kernels of Localities

A characterization of the 2-fusion system of L4(q)

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