A. Vasil’ev

activity

20182021

most citedFactoring nonabelian finite groups into two subsets

2 citations · 2 across the 3 of their papers we have counts for

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6 papers · 1 filter

math.GR2021

The closures of wreath products in product action

I. Ponomarenko, A. V. Vasil'ev

Let $m$ be a positive integer and let $Ω$ be a finite set. The $m$ -closure of $G \leq$ Sym $(Ω)$ is the largest permutation group on $Ω$ having the same orbits as $G$ in its induced ac…

math.GR2020★ 2 cited

Factoring nonabelian finite groups into two subsets

Ravil Bildanov, Vadim Goryachenko, Andrey Vasil'ev

A group $G$ is said to be factorized into subsets $A_{1}, A_{2}, \dots, A_{s} \subseteq G$ if every element $g$ in $G$ can be uniquely represented as $g = g_{1} g_{2} \dots g_{s}$ , where $g_i\in…

math.GR2019

The proper definition and Wielandt-Hartley's theorem for submaximal $X$ -subgroups

Danila Revin, Saveliy Skresanov, Andrey Vasil'ev

A nonempty class $X$ of finite groups is called complete if it is closed under taking subgroups, homomorphic images and extensions. We deal with a classical problem of d…

math.GR2018

The graph of atomic divisors and constructive recognition of finite simple groups

Alexander A. Buturlakin, Andrey V. Vasil'ev

The spectrum $ω (G)$ of a finite group $G$ is the set of orders of elements of $G$ . We present a polynomial-time algorithm that, given a finite set $M$ of positive integers…

math.GR2018

$2$ -Closure of $\frac{3}{2}$ -transitive group in polynomial time

Andrey V. Vasil'ev, Dmitry Churikov

Let $G$ be a permutation group on a finite set $Ω$ . The $k$ -closure $G^{(k)}$ of the group $G$ is the largest subgroup of $Sym (Ω)$ having the same orbits as $G$ on t…

math.GR2018

What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?

Elena K. Brusyanskaya, Anton A. Klyachko, Andrey V. Vasil'ev

Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation $x^{n} = 1$ in a group, the Solomon theorem (1969) on the number of solutio…

The closures of wreath products in product action

Factoring nonabelian finite groups into two subsets

The proper definition and Wielandt-Hartley's theorem for submaximal X-subgroups

The graph of atomic divisors and constructive recognition of finite simple groups

2-Closure of 23​-transitive group in polynomial time

What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?

The proper definition and Wielandt-Hartley's theorem for submaximal $X$ -subgroups

$2$ -Closure of $\frac{3}{2}$ -transitive group in polynomial time