Geodesic
On Ideals of the Group Algebra of an Infinite Symmetric Group over a Field of Characteristic~$p$
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 417-425.

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We prove that any nonzero ideal of the group algebra of the infinite symmetric group over a field of nonzero characteristic contains skew-symmetric and symmetric elements of sufficiently large order. Using this result, we reduce the question of the classification of the ideals of the group algebra of the infinite symmetric group to the classification of certain subspaces of the tensor square of a finitely generated free associative algebra.
Keywords: group algebra, ideal of a group algebra, multilinear polynomial, infinite symmetric group, finitely generated free associative algebra, tensor square. 
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     author = {A. R. Kemer},
     title = {On {Ideals} of the {Group} {Algebra} of an {Infinite} {Symmetric} {Group} over a {Field} of {Characteristic~}$p$},
     journal = {Matemati\v{c}eskie zametki},
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A. R. Kemer. On Ideals of the Group Algebra of an Infinite Symmetric Group over a Field of Characteristic~$p$. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 417-425. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a9/

[1] A. Kemer, “Multilinear identities of the algebras over a field of characteristic $p$”, Internat. J. Algebra Comput., 5:2 (1995), 189–197 | DOI | MR | Zbl