Ilya Gorshkov

collaborators

3 papers

math.GR2024

On groups whose conjugacy class sizes are not divisible by each other

Nanying Yang, Ilya Gorshkov

Let $G$ be a finite group and $N (G)$ be the set of its conjugacy class sizes excluding~ $1$ . Let us define a directed graph $Γ (G)$ , the set of vertices of this graph is $N (G)$ and t…

math.RA2024

Solid subalgebras in algebras of Jordan type half

I. Gorshkov, S. Shpectorov, A. Staroletov

The class of algebras of Jordan type $η$ was introduced by Hall, Rehren and Shpectorov in 2015 within the much broader class of axial algebras. Algebras of Jordan type are commutat…

math.GR2016

Thompson's conjecture for alternating group

Ilya Gorshkov

Let $G$ be a finite group, and let $N (G)$ be the set of sizes of its conjugacy classes. We show that if a finite group $G$ has trivial center and $N (G)$ equals to $N (A l t_{n})$ or $N(…