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- W4383723631 abstract "Abstract A group G is said to have restricted centralizers if for each the centralizer either is finite or has finite index in G . Shalev showed that a profinite group with restricted centralizers is virtually abelian. We take interest in profinite groups with restricted centralizers of uniform commutators, that is, elements of the form , where . Here, denotes the set of prime divisors of the order of . It is shown that such a group necessarily has an open nilpotent subgroup. We use this result to deduce that is finite if and only if the cardinality of the set of uniform k ‐step commutators in G is less than ." @default.
- W4383723631 created "2023-07-11" @default.
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- W4383723631 date "2023-07-09" @default.
- W4383723631 modified "2023-09-27" @default.
- W4383723631 title "Commutators, centralizers, and strong conciseness in profinite groups" @default.
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- W4383723631 doi "https://doi.org/10.1002/mana.202200320" @default.
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