Cristina Acciarri

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math.GR2026

Local--global generation property of commutators in finite $I ¨ $ -soluble groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a group $A$ acting by automorphisms on a group $G$ , let $I_{G} (A)$ denote the set of commutators $[g, a] = g^{- 1} g^{a}$ , where $g \in G$ and $a \in A$ , so that $[G, A]$ is the subgroup g…

math.GR2026

Rank type conditions on commutators in finite groups

Cristina Acciarri, Robert M. Guralnick, Evgeny Khukhro +1

For a subgroup $S$ of a group $G$ , let $I_{G} (S)$ denote the set of commutators $[g, s] = g^{- 1} g^{s}$ , where $g \in G$ and $s \in S$ , so that $[G, S]$ is the subgroup generated by $I_{G} (S)$ .…

math.GR2026

Profinite groups with restricted centralizers of powers

Cristina Acciarri, Pavel Shumyatsky

A group $G$ is said to have restricted centralizers if for every $x \in G$ the centralizer $C_{G} (x)$ either is finite or has finite index in $G$ . Shalev showed that a profinite group…

math.GR2026

Coprime commutators in profinite groups

Cristina Acciarri, Pavel Shumyatsky

By a coprime commutator in a profinite group $G$ we mean any element of the form $[x, y]$ , where $x, y \in G$ and $(∣ x ∣, ∣ y ∣) = 1$ . It is well-known that the subgroup generated by the c…

math.GR2024

Varieties of groups and the problem on conciseness of words

Cristina Acciarri, Pavel Shumyatsky

A group-word $w$ is concise in a class of groups $X$ if and only if the verbal subgroup $w (G)$ is finite whenever $w$ takes only finitely many values in a group $G\in \mat…

Local--global generation property of commutators in finite I¨-soluble groups

Rank type conditions on commutators in finite groups

Profinite groups with restricted centralizers of powers

Coprime commutators in profinite groups

Varieties of groups and the problem on conciseness of words

Local--global generation property of commutators in finite $I ¨ $ -soluble groups