N. Makarenko

activity

20082022

most citedFrobenius groups of automorphisms and their fixed points

22 citations · 47 across the 10 of their papers we have counts for

collaborators

11 papers

math.RA2022

Lie algebras with Frobenius dihedral groups of automorphisms

N. Yu. Makarenko

Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $F H$ with cyclic kernel $F$ and complement $H$ of order 2, such that the fixed-point subalgebra of $…

math.RA2021

Nilpotency of Lie type algebras with metacyclic Frobenius groups of automorphisms

N. Yu Makarenko

Suppose that a Lie type algebra L over a field K admits a Frobenius group of automorphisms FH with cyclic kernel F of order n and complement H such that the fixed-point subalgebra…

math.RA2017

Almost nilpotency of an associative algebra with an almost nilpotent fixed-point subalgebra

Makarenko Natalia

Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that…

math.RA2014

Lie type algebras with an automorphism of finite order

N. Yu. Makarenko

An algebra $L$ over a field $F$ , in which product is denoted by $[,]$ , is said to be \textit{ Lie type algebra} if for all elements $a, b, c \in L$ there exist $α, β\in \Bbb…

math.GR2014

Locally finite groups containing a $2$ -element with Chernikov centralizer

E. I. Khukhro, N. Yu. Makarenko, P. Shumyatsky

Suppose that a locally finite group $G$ has a $2$ -element $g$ with Chernikov centralizer. It is proved that if the involution in $⟨ g ⟩$ has nilpotent centralizer, then…

math.GR2014★ 2 cited

Finite groups and Lie rings with an automorphism of order $2^{n}$

E. I. Khukhro, N. Yu. Makarenko, P. Shumyatsky

Suppose that a finite group $G$ admits an automorphism $φ$ of order $2^{n}$ such that the fixed-point subgroup $C_{G} (φ^{2^{n - 1}})$ of the involution $φ^{2^{n - 1}}$ is nilpotent of clas…

math.GR2013

Finite p-groups with a Frobenius group of automorphisms whose kernel is a cyclic p-group

E. I. Khukhro, N. Yu. Makarenko

Suppose that a finite $p$ -group $P$ admits a Frobenius group of automorphisms $F H$ with kernel $F$ that is a cyclic $p$ -group and with complement $H$ . It is proved that if the fixe…

math.RA2013★ 4 cited

Lie algebras admitting a metacyclic Frobenius group of automorphisms

N. Yu. Makarenko, E. I. Khukhro

Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $F H$ with cyclic kernel $F$ and complement $H$ such that the characteristic of the ground field does…

math.GR2013★ 11 cited

Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms

E. I. Khukhro, N. Yu. Makarenko

Suppose that a finite group $G$ admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup $C_{G} (H)$ of t…

math.GR2010★ 22 cited

Frobenius groups of automorphisms and their fixed points

Evgenii I. Khukhro, Natalia Yu. Makarenko, Pavel Shumyatsky

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $F H$ with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial: $C_{G} (F) = 1$ .…

math.GR2008★ 8 cited

Automorphism invariance and identities

Evgenii I. Khukhro, Anton A. Klyachko, Natalia Yu. Makarenko +1

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras…