Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintarXiv licencearXiv

On finite simple groups possessing a conjugacy class of size 3p^n

  • Antonio Beltrán
  • Changguo Shao
Open at sourcePDFDOICite

Abstract

We classify all non-abelian finite simple groups that possess conjugacy classes of size 3pn for some prime p and non-negative integer n. As an application, we study the structure of the normal closure ⟨ gG⟩ of an element g in an arbitrary finite group G, provided that the conjugacy class gG has size 3pn. Specifically, we provide conditions for ⟨ gG⟩ to be solvable and completely determine its quotient modulo the solvable radical in the non-solvable case.

Related

  1. Sylow $2$-Subgroups of Finite Groups with a Single Conjugacy Class of Involutions
    Tianze Li, Yu Zeng
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Categorical and Floer-theoretic entropies: comparison and counting conjugacy classes in symplectic mapping class groups
    Sangjin Lee
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv
  3. The Conjugacy Problem for Recursively Presented Virtually Soluble Groups of Finite Prüfer Rank
    M. Brescia, E. Ingrosso, M. Trombetti
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  4. Finite groups with conjugacy classes of size 2pn
    Antonio Beltran, Changguo shao
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. On the number of conjugacy classes of finite solvable groups of order divisible by p2
    Thomas Michael Keller
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{beltran2026finite,
  title = {{On finite simple groups possessing a conjugacy class of size 3p^n}},
  author = {Antonio Beltrán and Changguo Shao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41488},
  eprint = {2610.41488},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41488},
}
RIS
TY  - UNPB
TI  - On finite simple groups possessing a conjugacy class of size 3p^n
AU  - Antonio Beltrán
AU  - Changguo Shao
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41488
UR  - https://arxiv.org/abs/2610.41488
AB  - We classify all non-abelian finite simple groups that possess conjugacy classes of size 3p^n for some prime p and non-negative integer n. As an application, we study the structure of the normal closure ⟨ g^G⟩ of an element g in an arbitrary finite group G, provided that the conjugacy class g^G has size 3p^n. Specifically, we provide conditions for ⟨ g^G⟩ to be solvable and completely determine its quotient modulo the solvable radical in the non-solvable case.
ER  -