Maximal ideals in modular group algebras of the finitary symmetric and 
alternating groups
Alexander Baranov 
Institute of Mathematics, Academy of Sciences of Belarus, Surganova 11, Minsk,
220072, Belarus 
and Alexander Kleshchev 
Department of Mathematics, University of Oregon, Eugene, Oregon 97403 

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.