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<p>A group <i>G</i> is said to have dense normalizers if every nonempty open interval in its subgroup lattice <i>L</i>(<i>G</i>) contains the normalizer of a certain subgroup of <i>G</i>. We find all finite groups satisfying this property. We also classify the finite groups, in which <i>k</i> subgroups are not normalizers for <i>k</i> = 1, 2, 3, 4.</p>

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Finite groups with many normalizers

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Marius Tărnăuceanu

摘要

A group G is said to have dense normalizers if every nonempty open interval in its subgroup lattice L(G) contains the normalizer of a certain subgroup of G. 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.