Abstract
We intend to generalize a crucial lemma of [4] to prove a somewhat surprising arithmetic property of profinite groups; namely, that a profinite group G has nontrivial p-Sylow-subgroups for only a finite number of primes if and only if this is true for its procyclic subgroups. This will yield as a corollary that every profinite torsion group has finite exponent if and only if this is true for its Sylow-sub-groups, a result also contained in [4].
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Herfort, W. An arithmetic property of profinite groups. Manuscripta Math 37, 11–17 (1982). https://doi.org/10.1007/BF01239941
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DOI: https://doi.org/10.1007/BF01239941