I. Gorshkov

activity

20132020

most citedRecognizability by spectrum of alternating groups

1 citations · 3 across the 4 of their papers we have counts for

collaborators

13 papers

math.GR2020

Finite skew braces with solvable additive group

Ilya Gorshkov, Timur Nasybullov

A. Smoktunowicz and L. Vendramin conjectured that if $A$ is a finite skew brace with solvable additive group, then the multiplicative group of $A$ is solvable. In this short note w…

math.RA2020

On primitive $3$ -generated axial algebras of Jordan type

Ilya Gorshkov, Alexey Staroletov

Axial algebras of Jordan type $η$ are commutative algebras generated by idempotents whose adjoint operators have the minimal polynomial dividing $(x - 1) x (x - η)$ , where $η\not\in\{0,1…

math.GR2019

On characterisation of a finite group by the set of conjugacy class sizes

Ilya Gorshkov

Let $G$ be a finite group and $N (G)$ be the set of its conjugacy class sizes. In the 1980's Thompson conjectured that the equality $N (G) = N (S)$ , where $Z (G) = 1$ and $S$ is simple, im…

math.RA2019

The geometric classification of nilpotent Tortkara algebras

Ilya Gorshkov, Ivan Kaygorodov, Mykola Khrypchenko

We give a geometric classification of all $6$ -dimensional nilpotent Tortkara algebras over $C$

math.GR2019

The group $J_{4} \times J_{4}$ is recognizable by spectrum

I. B. Gorshkov, N. V. Maslova

The spectrum of a finite group is the set of its element orders. In this paper we prove that the direct product of two copies of the finite simple sporadic group $J_{4}$ is uniquely…

math.RA2019

The algebraic classification of nilpotent Tortkara algebras