I. Gorshkov

activity

20242026

collaborators

7 papers

math.RA2026

Axial Algebras: Questions and Conjectures

I. Gorshkov, S. Shpectorov

Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead…

math.GR2026

Characterization of the alternating and symmetric groups by the order and conjugacy class sizes

Ilya Gorshkov, Andrey V. Vasil'ev

We prove that an arbitrary finite group $G$ having the same order and same set of conjugacy class sizes as an alternating or symmetric group $S$ must be isomorphic to $S$ . From thi…

math.GR2026

On {2,3,5}-groups with conjugacy classes of distinct sizes

Wei Zhou, Ilya Gorshkov

A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct sizes. In this paper, we show that if G is an ah-group and Ï(G) \subseteq {2,3,5},…

math.RA2026

Groups of generalized Moufang type and $Z_{2}$ -graded algebras

Ilya Gorshkov

A pair $(G, T)$ is called a faithful odd transposition group if $T$ is a normal set of involutions generating the group $G$ and the product of any two distinct elements of $T$ has o…

math.GR2025

On $A$ -Groups with the Same Index Set as a Nilpotent Group

Wei Zhou, Ilya Gorshkov

Let $G$ be a finite group and $N (G)$ be the set of conjugacy class sizes of $G$ . For a prime $p$ , let $∣ G ∣ ∣_{p}$ be the highest $p$ -power dividing some element of $N (G)$ . and define…

math.GR2025

On combinatorial properties of Gruenberg--Kegel graphs of finite groups

Mingzhu Chen, Ilya B. Gorshkov, Natalia V. Maslova +1

If $G$ is a finite group, then the spectrum $I ¨ (G)$ is the set of all element orders of $G$ . The prime spectrum $I ¨ (G)$ is the set of all primes belonging to $I ¨ (G)$ . A simple grap…