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- W4287281231 abstract "A coprime commutator in a profinite group $G$ is an element of the form $[x,y]$, where $x$ and $y$ have coprime order and an anti-coprime commutator is a commutator $[x,y]$ such that the orders of $x$ and $y$ are divisible by the same primes. In the present paper we establish that a profinite group $G$ is finite-by-pronilpotent if the cardinality of the set of coprime commutators in $G$ is less than $2^{aleph_0}$. Moreover, a profinite group $G$ has finite commutator subgroup $G'$ if the cardinality of the set of anti-coprime commutators in $G$ is less than $2^{aleph_0}$." @default.
- W4287281231 created "2022-07-25" @default.
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- W4287281231 date "2021-03-06" @default.
- W4287281231 modified "2023-09-23" @default.
- W4287281231 title "Strong conciseness of coprime and anti-coprime commutators" @default.
- W4287281231 doi "https://doi.org/10.48550/arxiv.2103.04061" @default.
- W4287281231 hasPublicationYear "2021" @default.
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