A. V. Vasil'ev

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math.GR2026

Multivalued Groups and Schur Rings

A. V. Vasil'ev, I. N. Ponomarenko

We study finite involutive multivalued groups associated with Schur rings. Their reduced valency is shown to equal the least common multiple of the sizes of the basic sets of the c…

math.GR2024

On multivalued groups of order 3

Jin Guo, Ilia Ponomarenko, Andrey V. Vasil'ev

A complete classification of the multivalued coset groups of order $3$ is given. The proof is based on the classification of rank $3$ groups having regular normal subgroups.

math.GR2024

Closures of permutation groups with restricted nonabelian composition factors

Ilia Ponomarenko, Saveliy V. Skresanov, Andrey V. Vasil'ev

Given a permutation group $G$ on a finite set $Ω$ , let $G^{(k)}$ denote the $k$ -closure of $G$ , that is, the largest permutation group on $Ω$ having the same orbits in the induced…