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arXiv · 2403.05774

On CLT and non-CLT groups

Marius Tărnăuceanu
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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.

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Marius Tărnăuceanu. 2024-03-09. On CLT and non-CLT groups. https://arxiv.org/abs/2403.05774

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