On Pro-p Cappitt Groups with finite exponent
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| Main Author: | |
|---|---|
| Publication Date: | 2024 |
| Other Authors: | |
| Format: | Article |
| Language: | eng |
| Source: | Repositório Institucional da UnB |
| Download full: | http://repositorio.unb.br/handle/10482/50390 https://doi.org/10.5802/crmath.562 https://orcid.org/0000-0002-8800-0827 |
Summary: | A pro-p Cappitt group is a pro-p group G such that Se(G) = 〈L ⩽c G |L ⋪G〉 is a proper subgroup (i.e. Se(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]). |