A pro- Cappitt group is a pro- group such that is a proper subgroup (i.e. ). In this paper we prove that non-abelian pro- 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- Cappitt group its subgroup commutator is a procyclic central subgroup. Finally we show that pro- Cappitt groups of exponent are pro- Dedekind groups. These results are pro- versions of the generalized Dedekind groups studied by Cappitt (see Theorem 1 and Lemma 7 in [1]).
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Mots clés : Generalized Dedekind groups, pro-$p$ Cappitt groups, torsion groups.
Anderson Porto 1, 2 ; Igor Lima 1, 2
@article{CRMATH_2024__362_G3_287_0, 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}, }
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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