Realizability and tameness of fusion systems

Institut for Matematiske Fag

Realizability and tameness of fusion systems

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Standard

Realizability and tameness of fusion systems. / Broto, Carles; Møller, Jesper M.; Oliver, Bob; Ruiz, Albert.

I: Proceedings of the London Mathematical Society, Bind 127, Nr. 6, 12.2023, s. 1816-1864.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Broto, C, Møller, JM, Oliver, B & Ruiz, A 2023, 'Realizability and tameness of fusion systems', Proceedings of the London Mathematical Society, bind 127, nr. 6, s. 1816-1864. https://doi.org/10.1112/plms.12571

APA

Broto, C., Møller, J. M., Oliver, B., & Ruiz, A. (2023). Realizability and tameness of fusion systems. Proceedings of the London Mathematical Society, 127(6), 1816-1864. https://doi.org/10.1112/plms.12571

Vancouver

Broto C, Møller JM, Oliver B, Ruiz A. Realizability and tameness of fusion systems. Proceedings of the London Mathematical Society. 2023 dec.;127(6):1816-1864. https://doi.org/10.1112/plms.12571

Author

Broto, Carles ; Møller, Jesper M. ; Oliver, Bob ; Ruiz, Albert. / Realizability and tameness of fusion systems. I: Proceedings of the London Mathematical Society. 2023 ; Bind 127, Nr. 6. s. 1816-1864.

Bibtex

@article{4f3c26f799b54ef6a698a04cce93f132,

title = "Realizability and tameness of fusion systems",

abstract = "A saturated fusion system over a finite (Formula presented.) -group (Formula presented.) is a category whose objects are the subgroups of (Formula presented.) and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over (Formula presented.) is realized by a finite group (Formula presented.) if (Formula presented.) is a Sylow (Formula presented.) -subgroup of (Formula presented.) and morphisms in the category are those induced by conjugation in (Formula presented.). One recurrent question in this subject is to find criteria as to whether a given saturated fusion system is realizable or not. One main result in this paper is that a saturated fusion system is realizable if all of its components (in the sense of Aschbacher) are realizable. Another result is that all realizable fusion systems are tame: a finer condition on realizable fusion systems that involves describing automorphisms of a fusion system in terms of those of some group that realizes it. Stated in this way, these results depend on the classification of finite simple groups, but we also give more precise formulations whose proof is independent of the classification.",

author = "Carles Broto and M{\o}ller, {Jesper M.} and Bob Oliver and Albert Ruiz",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",

year = "2023",

month = dec,

doi = "10.1112/plms.12571",

language = "English",

volume = "127",

pages = "1816--1864",

journal = "Proceedings of the London Mathematical Society",

issn = "0024-6115",

publisher = "Oxford University Press",

number = "6",

}

RIS

TY - JOUR

T1 - Realizability and tameness of fusion systems

AU - Broto, Carles

AU - Møller, Jesper M.

AU - Oliver, Bob

AU - Ruiz, Albert

PY - 2023/12

Y1 - 2023/12

N2 - A saturated fusion system over a finite (Formula presented.) -group (Formula presented.) is a category whose objects are the subgroups of (Formula presented.) and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over (Formula presented.) is realized by a finite group (Formula presented.) if (Formula presented.) is a Sylow (Formula presented.) -subgroup of (Formula presented.) and morphisms in the category are those induced by conjugation in (Formula presented.). One recurrent question in this subject is to find criteria as to whether a given saturated fusion system is realizable or not. One main result in this paper is that a saturated fusion system is realizable if all of its components (in the sense of Aschbacher) are realizable. Another result is that all realizable fusion systems are tame: a finer condition on realizable fusion systems that involves describing automorphisms of a fusion system in terms of those of some group that realizes it. Stated in this way, these results depend on the classification of finite simple groups, but we also give more precise formulations whose proof is independent of the classification.

AB - A saturated fusion system over a finite (Formula presented.) -group (Formula presented.) is a category whose objects are the subgroups of (Formula presented.) and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over (Formula presented.) is realized by a finite group (Formula presented.) if (Formula presented.) is a Sylow (Formula presented.) -subgroup of (Formula presented.) and morphisms in the category are those induced by conjugation in (Formula presented.). One recurrent question in this subject is to find criteria as to whether a given saturated fusion system is realizable or not. One main result in this paper is that a saturated fusion system is realizable if all of its components (in the sense of Aschbacher) are realizable. Another result is that all realizable fusion systems are tame: a finer condition on realizable fusion systems that involves describing automorphisms of a fusion system in terms of those of some group that realizes it. Stated in this way, these results depend on the classification of finite simple groups, but we also give more precise formulations whose proof is independent of the classification.

U2 - 10.1112/plms.12571

DO - 10.1112/plms.12571

M3 - Journal article

AN - SCOPUS:85175736550

VL - 127

SP - 1816

EP - 1864

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 6

ER -

ID: 381084486