Pavel Shumyatsky

activity

20122015

most citedOn profinite groups with Engel-like conditions

8 citations · 8 across the 5 of their papers we have counts for

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math.GR2015

On varieties of groups satisfying an Engel type identity

P. Shumyatsky, A. Tortora, M. Tota

Let m, n be positive integers, v a multilinear commutator word and w = v^m. Denote by v(G) and w(G) the verbal subgroups of a group G corresponding to v and w, respectively. We pro…

math.GR2015★ 8 cited

On profinite groups with Engel-like conditions

Raimundo Bastos, Pavel Shumyatsky

Let $G$ be a profinite group in which for every element $x \in G$ there exists a natural number $q = q (x)$ such that $x^{q}$ is Engel. We show that $G$ is locally virtually nilpotent. F…

math.GR2015

On the length of a finite group and of its 2-generator subgroups

Eloisa Detomi, Pavel Shumyatsky

The nonsoluble length $λ (G)$ of a finite group $G$ is defined as the minimum number of nonsoluble factors in a normal series of $G$ each of whose quotients either is soluble or is…

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.GR2012

On the Exponent of a Verbal Subgroup in a Finite Group