6 papers
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…
Cartesian products of graphs and their coherent configurations
Jinzhuan Cai, Jin Guo, Alexander L. Gavrilyuk +1
The coherent configuration of a graph is the smallest coherent configuration on the vertices of that contains the edge set of as a relation. The aim of…
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.
On the Weisfeiler-Leman dimension of circulant graphs
Yulai Wu, Ilia Ponomarenko
A circulant graph is a Cayley graph of a finite cyclic group. The Weisfeiler-Leman-dimension of a circulant graph with respect to the class of all circulant graphs is the small…
A linear programming bound for sum-rank metric codes
Aida Abiad, Alexander L. Gavrilyuk, Antonina P. Khramova +1
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances,…
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 induce…