Year: 2026
Type: article
Abstract: 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 with restricted centralizers is virtually abelian. Here we take interest in profinite groups G for which there is an integer n such that $$C_G(x^n)$$ is either finite or open whenever $$x\in G$$ . It is shown that such a group G has an open normal subgroup T with the property that G / Z ( T ) has finite exponent.
Authors: Cristina Acciarri, Pavel Shumyatsky
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7160715260