I. Gorshkov

activity

20132023

most citedThe algebraic classification of nilpotent Tortkara algebras

18 citations · 67 across the 18 of their papers we have counts for

collaborators

22 papers

math.RA2023

On Jordan algebras that are factors of Matsuo algebras

Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov

We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if F is a field of char…

math.GR2023★ 1 cited

On $p$ -index extremal groups

Andrey V. Vasil'ev, Ilya B. Gorshkov

The question on connection between the structure of a finite group $G$ and the properties of the indices of elements of $G$ has been a popular research topic for many years. The $p…

math.GR2022★ 3 cited

Structure of finite groups with restrictions on the set of conjugacy classes sizes

Ilya Gorshkov

Let $N (G)$ be the set of conjugacy classes sizes of $G$ . We prove that if $N (G) = Ω \times {1, n}$ for specific set $Ω$ of integers, then $G ≃ A \times B$ where $N (A) = Ω$ , $N(B)=\{…

math.RA2022

Quasi-definite axial algebras of Jordan type half

Ilya Gorshkov, Vsevolod Gubarev

Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents which action on an algebra is semisimple, and the fusion laws on the produ…

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★ 14 cited

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★ 1 cited

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★ 18 cited

The algebraic classification of nilpotent Tortkara algebras

Ilya Gorshkov, Ivan Kaygorodov, Mykola Khrypchenko

We classify all $6$ -dimensional nilpotent Tortkara algebras over $C .$

math.GR2018★ 3 cited

On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes

Ilya Gorshkov

The greatest power of a prime $p$ dividing the natural number $n$ will be denoted by $n_{p}$ . Let $I n d_{G} (g) = ∣ G : C_{G} (g) ∣$ . Suppose that $G$ is a finite group and $p$ is a prime. We pro…

math.GR2018

On Thompson's conjecture for finite simple groups

Ilya Gorshkov

Let $G$ be a finite group, $N (G)$ be the set of conjugacy classes of the group $G$ . In the present paper it is proved $G ≃ L$ if $N (G) = N (L)$ , where $G$ is a finite group with t…

math.GR2018★ 1 cited

On a connection between the order of a finite group and the set of conjugacy classes size

I. B. Gorshkov

Let $G \in {p, q}^{*}$ be a finite group with trivial center, where $p, q \in π (G)$ and $p > q > 5$ . In the present paper it is proved that $∣ G ∣_{{p, q}} = ∣ G ∣ ∣_{{p, q}}$ ; in particular $C_G…

math.GR2018★ 5 cited

On groups having the prime graph as alternating and symmetric groups

Ilya Gorshkov, Alexey Staroletov

The {\it prime graph} $Γ (G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $∣ G ∣$ and in which two distinct vertices $r$ and $s$ are adjacent i…

math.GR2017★ 1 cited

On Thompson's conjecture for finite simple exceptional groups of Lie type

Ilya Gorshkov, Ivan Kaygorodov, Andrei Kukharev +1

Let $G$ be a finite group, $N (G)$ be the set of conjugacy classes of the group $G$ . In the present paper it is proved $G ≃ L$ if $N (G) = N (L)$ , where $G$ is a finite group with t…

math.RA2017★ 17 cited

Degenerations of Jordan Algebras and ''Marginal'' Algebras

Ilya Gorshkov, Ivan Kaygorodov, Yury Popov

We describe all degenerations of the variety $Jord_{3}$ of Jordan algebras of dimension three over $C .$ In particular, we describe all irreducible components in $…

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(…

math.GR2016★ 1 cited

On Thompson's conjecture for alternating group of large degree

Ilya Gorshkov

For a finite group $G$ , let $N (G)$ denote the set of conjugacy class sizes of $G$ . We show that if every finite group $G$ with trivial center such that $N (G)$ equals to $N (A l t_{n})$ ,…

math.GR2016

Finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of solvable groups

Ilya B. Gorshkov, Natalia V. Maslova

In this paper we describe all the finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of finite solvable groups.

math.GR2015

A Moufang loop with exceptional properties of associators

Ilya B. Gorshkov, Alexandre N. Grichkov, Andrei V. Zavarnitsine

We construct a Moufang loop $M$ of order $3^{19}$ and a pair $a, b$ of its elements such that the set of all elements of $M$ that associate with $a$ and $b$ does not form a subloop.…

math.GR2015★ 1 cited

On Thompson's conjecture for alternating and symmetric groups

Ilya B. Gorshkov

For a finite group $G$ denote by $N (G)$ the set of conjugesy class sizes of $G$ . We show that every finite group $G$ with the property $N (G) = N (A l t_{n}), n > 4$ or $N (G) = N (S y m_{n}), n > 22$ …

math.GR2013★ 1 cited

Recognizability by spectrum of alternating groups

I. B. Gorshkov

The spectrum of a group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group that has the same spectrum as $G$ is isomo…

On Jordan algebras that are factors of Matsuo algebras

On p-index extremal groups

Structure of finite groups with restrictions on the set of conjugacy classes sizes

Quasi-definite axial algebras of Jordan type half

Finite skew braces with solvable additive group

On primitive 3-generated axial algebras of Jordan type

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

The geometric classification of nilpotent Tortkara algebras

The group J4​×J4​ is recognizable by spectrum

The algebraic classification of nilpotent Tortkara algebras

On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes

On Thompson's conjecture for finite simple groups

On a connection between the order of a finite group and the set of conjugacy classes size

On groups having the prime graph as alternating and symmetric groups

On Thompson's conjecture for finite simple exceptional groups of Lie type

Degenerations of Jordan Algebras and ''Marginal'' Algebras

Thompson's conjecture for alternating group

On Thompson's conjecture for alternating group of large degree

Finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of solvable groups

A Moufang loop with exceptional properties of associators

On Thompson's conjecture for alternating and symmetric groups

Recognizability by spectrum of alternating groups

On $p$ -index extremal groups

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

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