4 papers
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…
On multivalued groups of order 3
Jin Guo, Ilia Ponomarenko, Andrey V. Vasil'ev
A complete classification of the multivalued coset groups of order is given. The proof is based on the classification of rank groups having regular normal subgroups.
The automorphism groups of small affine rank 3 graphs
Jin Guo, Andrey V. Vasil'ev, Rui Wang
A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent mono…
Closures of permutation groups with restricted nonabelian composition factors
Ilia Ponomarenko, Saveliy V. Skresanov, Andrey V. Vasil'ev
Given a permutation group on a finite set , let denote the -closure of , that is, the largest permutation group on having the same orbits in the induced…