I. Gorshkov

activity

20202026

most citedOn

3

-generated axial algebras of Jordan type

\frac{1}{2}

1 citations · 1 across the 12 of their papers we have counts for

collaborators

14 papers

math.GR2026

On the order of a finite group with trivial centre and bounded conjugacy classes

Ilya Gorshkov

A group is called an $n$ -$\bfc$-group if each of its conjugacy classes is finite and contains at most $n$ elements. By a theorem of B.~H.~Neumann the derived subgroup of such a gro…

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 π(G) \subseteq {2,3,5}, w…

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.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.GR2024

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 $ω (G)$ is the set of all element orders of $G$ . The prime spectrum $π (G)$ is the set of all primes belonging to $ω (G)$ . A simple graph $…

math.RA2023

Automorphism groups of axial algebras

Ilya Gorshkov, Justin McInroy, Tendai Mudziiri Shumba +1

Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess alge…

math.RA2023★ 1 cited

On $3$ -generated axial algebras of Jordan type $\frac{1}{2}$

Ravil Bildanov, Ilya Gorshkov

Axial algebras of Jordan type $η$ are a special type of commutative non-associative algebras. They are generated by idempotents whose adjoint operators have the minimal polynomial…

math.RA2023

Axial view on pseudo-composition algebras and train algebras of rank 3

Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov

We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompos…

math.GR2022

On recognition of direct powers of finite simple linear groups by spectrum

N. Yang, I. B. Gorshkov, A. M. Staroletov +1

The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive intege…

math.GR2020

Characterization of groups with non-simple socle

Ilya Gorshkov

The spectrum of a finite group is a set of its element orders. We prove that if $m > 5$ then the group $L_{2^{m}} (2) \times L_{2^{m}} (2) \times L_{2^{m}} (2)$ is uniquely determined by its sp…

On the order of a finite group with trivial centre and bounded conjugacy classes

Axial Algebras: Questions and Conjectures

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

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

Groups of generalized Moufang type and Z2​-graded algebras

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

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

Solid subalgebras in algebras of Jordan type half

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

Automorphism groups of axial algebras

On 3-generated axial algebras of Jordan type 21​

Axial view on pseudo-composition algebras and train algebras of rank 3

On recognition of direct powers of finite simple linear groups by spectrum

Characterization of groups with non-simple socle

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

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

On $3$ -generated axial algebras of Jordan type $\frac{1}{2}$