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

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6 papers · 1 filter

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.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…

Locally finite groups containing a 2-element with Chernikov centralizer