Comptes Rendus
Article de recherche - Théorie des groupes
On Pro-p Cappitt Groups with finite exponent
Anderson Porto1, 2  ; Igor Lima1, 2
1 Instituto de Ciência e Tecnologia - ICT, Universidade Federal dos Vales do Jequitinhonha e Mucuri, Diamantina - MG, 39100-000 Brazil
2 Departamento de Matemática, Universidade de Brasília, Brasilia-DF, 70910-900 Brazil
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 287-292.

A pro-p Cappitt group is a pro-p group G such that S ˜(G)=〈L⩽ c G|L⋪G〉 ¯ is a proper subgroup (i.e. 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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DOI : 10.5802/crmath.562
Classification : 20E34, 20E18
Mots clés : Generalized Dedekind groups, pro-$p$ Cappitt groups, torsion groups.
Anderson Porto 1, 2 ; Igor Lima 1, 2

1 Instituto de Ciência e Tecnologia - ICT, Universidade Federal dos Vales do Jequitinhonha e Mucuri, Diamantina - MG, 39100-000 Brazil
2 Departamento de Matemática, Universidade de Brasília, Brasilia-DF, 70910-900 Brazil
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Anderson Porto and Igor Lima},
     title = {On {Pro-}$p$ {Cappitt} {Groups} with finite exponent},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {287--292},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.562},
     language = {en},
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Anderson Porto; Igor Lima. On Pro-$p$ Cappitt Groups with finite exponent. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 287-292. doi : 10.5802/crmath.562. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.562/

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