On the blockwise modular isomorphism problem

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Gabriel Navarro
  • Benjamin Sambale

Externe Organisationen

  • Universitat de Valencia
  • Technische Universität Kaiserslautern
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)263-278
Seitenumfang16
FachzeitschriftManuscripta mathematica
Jahrgang157
Ausgabenummer1-2
PublikationsstatusVeröffentlicht - 1 Sept. 2018
Extern publiziertJa

Abstract

As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. Over a valuation ring of characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.

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On the blockwise modular isomorphism problem. / Navarro, Gabriel; Sambale, Benjamin.
in: Manuscripta mathematica, Jahrgang 157, Nr. 1-2, 01.09.2018, S. 263-278.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Navarro G, Sambale B. On the blockwise modular isomorphism problem. Manuscripta mathematica. 2018 Sep 1;157(1-2):263-278. doi: 10.1007/s00229-017-0990-z
Navarro, Gabriel ; Sambale, Benjamin. / On the blockwise modular isomorphism problem. in: Manuscripta mathematica. 2018 ; Jahrgang 157, Nr. 1-2. S. 263-278.
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