4 papers · 1 filter
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…
Notes on -groups
Ilia Ponomarenko, Grigory Ryabov
Following Wielandt, a finite group is called a -group (Burnside group) if every primitive group containing a regular subgroup isomorphic to is doubly transitive. Using a…
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.
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…