Statistiques sur le groupe symétrique
A group G is strongly bounded if every isometric action of G on a metric space has bounded orbits. We show that the automorphism groups of typical countable structures with the small index property are strongly bounded. In particular we show that this is the case when G is the automorphism group of the countable universal locally finite extension of a periodic abelian group.
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....