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• W1552144443 abstract "The main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups (provided the characteristic $p$ of the ground field is greater than 2). For the symmetric group there are exactly $p-1$ such ideals and for the alternating group there are $(p-1)/2$ of them. The description is obtained in terms of the annihilators of certain systems of the ‘completely splittable’ irreducible modular representations of the finite symmetric and alternating groups. The main tools used in the proofs are the modular branching rules (obtained earlier by the second author) and the ‘Mullineux conjecture’ proved recently by Ford-Kleshchev and Bessenrodt-Olsson. The results obtained are relevant to the theory of PI-algebras. They are used in a later paper by the authors and A. E. Zalesskii on almost simple group algebras and asymptotic properties of modular representations of symmetric groups." @default.
• W1552144443 created "2016-06-24" @default.
• W1552144443 creator A5020241451 @default.
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• W1552144443 date "1999-01-01" @default.
• W1552144443 modified "2023-09-25" @default.
• W1552144443 title "Maximal ideals in modular group algebras of the finitary symmetric and alternating groups" @default.
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• W1552144443 doi "https://doi.org/10.1090/s0002-9947-99-02003-6" @default.
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