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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 $𝔽 S_{n}$ of the symmetric group $S_{n}$ over a field $𝔽$ of characteristic 0 (or $p > n$ ). The goal is to obtain a constructive version of the isomorphism $ψ : ⨁_{λ} M_{d_{λ}} (𝔽) ⟶ 𝔽 S_{n}$ where $λ$ is a partition of $n$ and $d_{λ}$ counts the standard tableaux of shape $λ$ ....

Subgroup embeddings in the symmetric group of degree nine.

Mysovskikh, V.I., Skopin, A.I. (2002)

Zapiski Nauchnykh Seminarov POMI

Transitive 3-groups of degree $3^{n}$ (n = 2,3)

M. S. Audu, A. Afolabi, E. Apine (2006)

Kragujevac Journal of Mathematics

Displaying 1 – 7 of 7

A GAP package for braid orbit computation and applications.

Block systems of a Galois group.

Finding the automorphism group of a circulant association scheme in polynomial time.

Simple groups in computational group theory.

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Subgroup embeddings in the symmetric group of degree nine.

Transitive 3-groups of degree 3 n (n = 2,3)

Currently displaying 1 – 7 of 7

Transitive 3-groups of degree $3^{n}$ (n = 2,3)