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Mathematics > Group Theory

Title: On pro-p Cappitt groups with finite exponent

Abstract: A pro-p Cappitt group is a pro-p group G such that the subgroup topologically generated by all non-normal closed subgroups is a proper subgroup of G. In this paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is closed has finite exponent. 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.
Subjects: Group Theory (math.GR)
MSC classes: 20E34, 20E18
Cite as: arXiv:2309.00914 [math.GR]
  (or arXiv:2309.00914v1 [math.GR] for this version)

Submission history

From: Anderson Porto [view email]
[v1] Sat, 2 Sep 2023 11:27:48 GMT (14kb)

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