Skip to content
DraconiticResearch
Search Sources API
190,851 studies31 sourcesUpdated 11 min ago
PreprintCC BY-NC-SA 4.0arXiv

The prime graph complements of π’œ11- and π’œ13-solvable groups

  • Logan Abounader
  • Austin Bell
  • April Beun
  • Elvis Cabrera
  • Dakota Nobuyuki Goto
  • Thomas Michael Keller
Open at sourcePDFDOICite

Abstract

We study prime graph complements of π’œn-solvable groups, focusing on the cases π’œ11 and π’œ13. These provide the first classifications of T-solvable groups for which |Ο€(T)|>4. We develop structural and representation-theoretic tools for analyzing the possible prime graph complements and use them to obtain complete characterizations for both π’œ11-solvable and π’œ13-solvable groups. The methods introduced also provide a framework for studying analogous classification problems for larger alternating groups.

Related

  1. Prime-order complements in planar graph Jacobians
    Anass Nifa
    HALPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsHAL
  2. Prime Graphs of Locally Torsion Ultragroups, Metanilpotent Groups, and T-Solvable Groups
    Alexa Renner
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Finite abelian groups are Schur multipliers of finite solvable groups
    Derek F. Holt
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryarXiv
  4. The Eaton--MoretΓ³ Conjecture Holds True for p-Solvable Groups
    Yanjun Liu, Lizhong Wang, Jiping Zhang +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Sharp Hausdorff--Young inequalities for solvable and semisimple Lie groups
    Jinsong Wu, Fulin Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{abounader2026prime,
  title = {{The prime graph complements of $\mathcalA_11$- and $\mathcalA_13$-solvable groups}},
  author = {Logan Abounader and Austin Bell and April Beun and Elvis Cabrera and Dakota Nobuyuki Goto and Thomas Michael Keller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24325},
  eprint = {2610.24325},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24325},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - The prime graph complements of π’œ_11- and π’œ_13-solvable groups
AU  - Logan Abounader
AU  - Austin Bell
AU  - April Beun
AU  - Elvis Cabrera
AU  - Dakota Nobuyuki Goto
AU  - Thomas Michael Keller
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.24325
UR  - https://arxiv.org/abs/2610.24325
AB  - We study prime graph complements of π’œ_n-solvable groups, focusing on the cases π’œ_11 and π’œ_13. These provide the first classifications of T-solvable groups for which |Ο€(T)|>4. We develop structural and representation-theoretic tools for analyzing the possible prime graph complements and use them to obtain complete characterizations for both π’œ_11-solvable and π’œ_13-solvable groups. The methods introduced also provide a framework for studying analogous classification problems for larger alternating groups.
ER  -