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- W3044125835 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.
- W3044125835 created "2020-07-29" @default.
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- W3044125835 date "2020-07-22" @default.
- W3044125835 modified "2023-10-05" @default.
- W3044125835 title "Strong conciseness of coprime and anti-coprime commutators" @default.
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- W3044125835 doi "https://doi.org/10.1007/s10231-020-01020-2" @default.
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