V. S. Atabekyan

activity

20132026

most citedCentral extensions of free periodic groups

9 citations · 30 across the 5 of their papers we have counts for

collaborators

6 papers

math.GR2026

Mazurov's question on fixed points of automorphisms of free Burnside groups

V. S. Atabekyan

In the Kourovka Notebook, V.\,D.~Mazurov asked whether an automorphism $α$ of prime order $m$ of the infinite free Burnside group $G = B (m, q)$ of prime period $q$ that cyclically per…

math.GR2018★ 9 cited

Central extensions of free periodic groups

Srgei I. Adian, Varujan S. Atabekyan

It is proved that any countable abelian group $D$ can be embedded as a centre into a $m$ -generated group $A$ such that the quotient group $A / D$ is isomorphic to the free Burnside g…

math.GR2015★ 6 cited

Automorphism groups of endomorphism semigroups of free periodic groups

Varujan S. Atabekyan

In this paper we describe the automorphism groups of the endomorphism semigroups of free Burnside groups $B (m, n)$ for odd exponents $n \geq 1003$ . We prove, that the groups $Aut(End(B…

math.GR2015★ 6 cited

The Hopfian Property of $n$ -Periodic Products of Groups

S. I. Adian, V. S. Atabekyan

Let $H$ be a subgroup of a group $G$ . A normal subgroup $N_{H}$ of $H$ is said to be inheritably normal if there is a normal subgroup $N_{G}$ of $G$ such that $N_{H} = N_{G} \cap H$ . It is pr…

math.GR2014★ 3 cited

Splitting automorphisms of prime power orders of free Burnside groups

Varujan S. Atabekyan

We prove that if the order of a splitting automorphism of free Burnside group~ $B (m, n)$ of odd period~ $n \geq 1003$ is a prime power, then the automorphism is inner. Thus, we give an a…

math.GR2013★ 6 cited

Automorphism tower problem and semigroup of endomorphisms for free Burnside groups

Varujan Atabekyan

We have proved that the group of all inner automorphisms of the free Burnside group $B (m, n)$ is the unique normal subgroup in $A u t (B (m, n))$ among all its subgroups, which are isomo…