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PreprintCC BY 4.0arXiv

Supersoluble groups and the probability of generating a supersoluble subgroup

  • Andrea Lucchini
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Abstract

Let G be a finite group and let P𝒰(G) denote the probability that two randomly chosen elements of G generate a supersoluble subgroup. We prove that if P𝒰(G) > 16/25 then G is supersoluble, and that the bound 16/25 is sharp, being attained by the group G = (C5 Γ— C5) rtimes Q8, where Q8 acts faithfully and irreducibly on C5 Γ— C5.

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Cite

BibTeXRIS
BibTeX
@misc{lucchini2026supersoluble,
  title = {{Supersoluble groups and the probability of generating a supersoluble subgroup}},
  author = {Andrea Lucchini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.08165},
  eprint = {2607.08165},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.08165},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Supersoluble groups and the probability of generating a supersoluble subgroup
AU  - Andrea Lucchini
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2607.08165
UR  - https://arxiv.org/abs/2607.08165
AB  - Let G be a finite group and let P_𝒰(G) denote the probability that two randomly chosen elements of G generate a supersoluble subgroup. We prove that if P_𝒰(G) > 16/25 then G is supersoluble, and that the bound 16/25 is sharp, being attained by the group G = (C_5 Γ— C_5) rtimes Q_8, where Q_8 acts faithfully and irreducibly on C_5 Γ— C_5.
ER  -