Profinite Dedekind Groups

Porto, Anderson Luiz Pedrosa; Bessa, Vagner Rodrigues de

doi:10.17654/ms126010089

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2024

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“…In the profinite version, as in [7] and [8], a profinite Dedekind group will be a profinite group in which every closed subgroup is normal. A profinite non-abelian Dedekind group will be called a profinite Hamiltonian group.…”

Section: Preliminariesmentioning

confidence: 99%

On Pro-p Cappitt Groups with finite exponent

Porto,

Lima

2024

Comptes Rendus. Mathématique

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S(G) ̸ = G).In this paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is closed and it has finite exponent. This result is a natural continuation of main result of the first author [7]. We also prove that in a pro-p Cappitt group its subgroup commutator is a procyclic central subgroup. Finally we show that pro-2 Cappitt groups of exponent 4 are pro-2 Dedekind groups. These results are pro-p versions of the generalized Dedekind groups studied by Cappitt (see Theorem 1 and Lemma 7 in [1]).

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Section: Preliminariesmentioning

confidence: 99%