18 papers
Polynomial-time isomorphism test for -generated extensions of abelian groups
Saveliy V. Skresanov
The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific gro…
On finite groups with exactly one noncommutator
Saveliy V. Skresanov
An element of a group is a commutator if it can be expressed in the form for some . In 2010 MacHale posed the following problem in the Kour…
Rota-Baxter operators on compact simple Lie groups and algebras
Saveliy V. Skresanov
A Rota-Baxter operator on a Lie group is a smooth map such that for all . This concept was introduced in 2021…
Reduction of the group isomorphism problem to the group automorphism problem
Saveliy V. Skresanov
It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We s…
Random unipotent Sylow subgroups of groups of Lie type of bounded rank
Saveliy V. Skresanov
In 2001 Liebeck and Pyber showed that a finite simple group of Lie type is a product of carefully chosen unipotent Sylow subgroups. Later, in a series of works it was shown…
Expanders and growth of normal subsets in finite simple groups of Lie type
Saveliy V. Skresanov
We show that some classical results on expander graphs imply growth results on normal subsets in finite simple groups. As one application, it is shown that given a nontrivial norma…