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arXiv · 2503.22966

Finite groups with many normalizers

Marius Tărnăuceanu
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Abstract

A group $G$ is said to have dense normalizers if each non-empty open interval in its subgroup lattice $L(G)$ contains the normalizer of a certain subgroup of $G$. In this note, we find all finite groups satisfying this property. We also classify the finite groups in which $k$ subgroups are not normalizers, for $k=1,2,3,4$.

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Marius Tărnăuceanu. 2025-03-29. Finite groups with many normalizers. https://arxiv.org/abs/2503.22966

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