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Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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OriginalspracheEnglisch
Seiten (von - bis)439-463
Seitenumfang24
FachzeitschriftAnnals of Representation Theory
Jahrgang1
Ausgabenummer3
Frühes Online-Datum3 Okt. 2024
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 3 Okt. 2024

Abstract

We classify principal -blocks of finite groups with Sylow -subgroups isomorphic to a wreathed -group with up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig’s Finiteness Conjecture holds for such blocks. Furthermore, we obtain a classification of such groups modulo , which is a purely group theoretical result and of independent interest. Methods previously applied to blocks of tame representation type are used. They are, however, further developed in order to deal with blocks of wild representation type.

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Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence. / Koshitani, Shigeo; Lassueur, Caroline; Sambale, Benjamin.
in: Annals of Representation Theory, Jahrgang 1, Nr. 3, 03.10.2024, S. 439-463.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Koshitani, S., Lassueur, C., & Sambale, B. (2024). Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence. Annals of Representation Theory, 1(3), 439-463. Vorabveröffentlichung online. https://doi.org/10.48550/arXiv.2310.13621, https://doi.org/10.5802/art.16
Koshitani S, Lassueur C, Sambale B. Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence. Annals of Representation Theory. 2024 Okt 3;1(3):439-463. Epub 2024 Okt 3. doi: 10.48550/arXiv.2310.13621, 10.5802/art.16
Koshitani, Shigeo ; Lassueur, Caroline ; Sambale, Benjamin. / Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence. in: Annals of Representation Theory. 2024 ; Jahrgang 1, Nr. 3. S. 439-463.
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T1 - Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

AU - Koshitani, Shigeo

AU - Lassueur, Caroline

AU - Sambale, Benjamin

N1 - (c) The authors, 2024

PY - 2024/10/3

Y1 - 2024/10/3

N2 - We classify principal -blocks of finite groups with Sylow -subgroups isomorphic to a wreathed -group with up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig’s Finiteness Conjecture holds for such blocks. Furthermore, we obtain a classification of such groups modulo , which is a purely group theoretical result and of independent interest. Methods previously applied to blocks of tame representation type are used. They are, however, further developed in order to deal with blocks of wild representation type.

AB - We classify principal -blocks of finite groups with Sylow -subgroups isomorphic to a wreathed -group with up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig’s Finiteness Conjecture holds for such blocks. Furthermore, we obtain a classification of such groups modulo , which is a purely group theoretical result and of independent interest. Methods previously applied to blocks of tame representation type are used. They are, however, further developed in order to deal with blocks of wild representation type.

KW - Morita equivalences

KW - wreathed Sylow 2-subgroups

KW - Splendid Morita equivalence

KW - source-algebra equivalence

KW - trivial source modules

KW - Projective special linear group

KW - Projective special unitary group

U2 - 10.48550/arXiv.2310.13621

DO - 10.48550/arXiv.2310.13621

M3 - Article

VL - 1

SP - 439

EP - 463

JO - Annals of Representation Theory

JF - Annals of Representation Theory

SN - 2704-2081

IS - 3

ER -

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