8 citations · 15 across the 6 of their papers we have counts for
9 papers
The closures of wreath products in product action
I. Ponomarenko, A. V. Vasil'ev
Let be a positive integer and let be a finite set. The -closure of Sym is the largest permutation group on having the same orbits as in its induced ac…
The -closure of a solvable permutation group is solvable
E. A. O'Brien, I. Ponomarenko, A. V. Vasil'ev +1
Let be a positive integer and let be a finite set. The -closure of is the largest permutation group on having the same orbits as in…
On Schur 2-groups
Mikhail Muzychuk, Ilya Ponomarenko
A finite group is called a Schur group, if any Schur ring over is the transitivity module of a point stabilizer in a subgroup of $\sym(G)$ that contains all right translati…
On separability problem for circulant S-rings
Sergei Evdokimov, Ilya Ponomarenko
A Schur ring (S-ring) over a group is called separable if every of its similaritities is induced by isomorphism. We establish a criterion for an S-ring to be separable in the c…
Coset closure of a circulant S-ring and schurity problem
Sergei Evdokimov, Ilya Ponomarenko
Let be a finite group. There is a natural Galois correspondence between the permutation groups containing as a regular subgroup, and the Schur rings (S-rings) over~. The…
On non-abelian Schur groups
Ilya Ponomarenko, Andrey Vasil'ev
A finite group G is called Schur, if every Schur ring over G is associated in a natural way with a regular subgroup of Sym(G) that is isomorphic to G. We prove that any nonabelian…
On schurity of finite abelian groups
Sergei Evdokimov, István Kovács, Ilya Ponomarenko
A finite group is called a Schur group, if any Schur ring over is associated in a natural way with a subgroup of that contains all right translations. Recently, th…
Characterization of cyclic Schur groups
Sergei Evdokimov, István Kovács, Ilya Ponomarenko
A finite group is called a Schur group, if any Schur ring over is the transitivity module of a permutation group on the set containing the regular subgroup of all right…
Schurity of S-rings over a cyclic group and generalized wreath product of permutation groups
Sergei Evdokimov, Ilya Ponomarenko
The generalized wreath product of permutation groups is introduced. By means of it we study the schurity problem for S-rings over a cyclic group and the automorphism groups of…