I. Gorshkov

activity

20132023

most citedRecognizability by spectrum of alternating groups

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

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10 papers · 1 filter

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.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.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.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

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

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…

Finite skew braces with solvable additive group

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

The group J4​×J4​ is recognizable by spectrum

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

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