Finite groups whose subgroup graph contains a vertex of large degree

Marius Tărnăuceanu

Finite groups whose subgroup graph contains a vertex of large degree

Group Theory 2025-02-05 v2

Authors: Marius Tărnăuceanu

Abstract

T.C. Burness and S.D. Scott \cite{3} classified finite groups $G$ such that the number of prime order subgroups of $G$ is greater than $|G|/2-1$ . In this note, we study finite groups $G$ whose subgroup graph contains a vertex of degree greater than $|G|/2-1$ . The classification given for finite solvable groups extends the work of Burness and Scott.

Keywords

finite group theory graph theory of groups group theory

Cite

@article{arxiv.2412.18087,
  title  = {Finite groups whose subgroup graph contains a vertex of large degree},
  author = {Marius Tărnăuceanu},
  journal= {arXiv preprint arXiv:2412.18087},
  year   = {2025}
}

Comments

Accepted for publication in Arch. Math

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