On CLT and non-CLT groups

Marius Tărnăuceanu

On CLT and non-CLT groups

Group Theory 2024-03-12 v1

Authors: Marius Tărnăuceanu

Abstract

In this note, we prove that for every integer $d\geq 2$ which is not a prime power, there exists a finite solvable group $G$ such that $d\mid |G|$ , $\pi(G)=\pi(d)$ and $G$ has no subgroup of order $d$ . We also introduce the CLT-degree of a finite group and answer two questions about it.

Keywords

finite group theory finite groups group theory

Cite

@article{arxiv.2403.05774,
  title  = {On CLT and non-CLT groups},
  author = {Marius Tărnăuceanu},
  journal= {arXiv preprint arXiv:2403.05774},
  year   = {2024}
}

Comments

Accepted for publication in Ann. Mat. Pura Appl

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