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PreprintCC BY 4.0arXiv

Profinite groups whose closed subgroups are subnormal of defect at most two

  • A. L. P. Porto
  • I. Lima
  • M. Silva
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Abstract

In this paper, we classify profinite groups whose closed subgroups are subnormal of defect at most two, providing profinite versions of theorems due to Heineken and to Mahdavianary. We also establish that if G is a finitely generated periodic pro-π group, where π is a finite set of odd primes, and all its procyclic subgroups are subnormal of defect at most 2, then G is a finite π-group in which every abelian subgroup is subnormal of defect at most 2.

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Cite

BibTeXRIS
BibTeX
@misc{porto2026profinite,
  title = {{Profinite groups whose closed subgroups are subnormal of defect at most two}},
  author = {A. L. P. Porto and I. Lima and M. Silva},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31878},
  eprint = {2610.31878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31878},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Profinite groups whose closed subgroups are subnormal of defect at most two
AU  - A. L. P. Porto
AU  - I. Lima
AU  - M. Silva
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31878
UR  - https://arxiv.org/abs/2610.31878
AB  - In this paper, we classify profinite groups whose closed subgroups are subnormal of defect at most two, providing profinite versions of theorems due to Heineken and to Mahdavianary. We also establish that if G is a finitely generated periodic pro-π group, where π is a finite set of odd primes, and all its procyclic subgroups are subnormal of defect at most 2, then G is a finite π-group in which every abelian subgroup is subnormal of defect at most 2.
ER  -