Mathematica Bohemica

Mathematica Bohemica, first online, pp. 1-9

On the lattice of U-normal subgroups of dihedral groups

Shailesh SINGH, Vilas KHARAT, Manish AGALAVE

Received May 29, 2025. Published online April 7, 2026.

Abstract: We classify abnormal and U-normal subgroups of the dihedral group for any positive integer $n$. We establish necessary and sufficient criteria for the collection of abnormal and U-normal subgroups to form a lattice, highlighting that while U-normal subgroups constitute a lattice, it is not a sublattice of the lattice of all subgroups of the group. Futhermore, we provide a comprehensive enumeration of the sizes of these collections, offering new insights into the structural properties of dihedral groups.

Keywords: abnormal subgroup; U-normal subgroup; dihedral group

Classification MSC: 06A06, 06A07, 06B20, 06B23, 20D25, 20D30, 20D40, 20E15, 20F22, 20K27

DOI: 10.21136/MB.2026.0077-25

PDF available at: Institute of Mathematics CAS

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Affiliations: Shailesh Singh (corresponding author), Department of Mathematics, S. P. Pune University, Pune 411007, India and Department of Mathematics and Statistics, Somaiya School of Basic and Applied Sciences, SVU, Mumbai 400077, India, e-mail: shaileshsingh.sha04@gmail.com; Vilas Kharat, Department of Mathematics, S. P. Pune University, Pune 411007, India; Manish Agalave, Department of Mathematics, Fergusson College (Autonomous), F. C. Road, Pune 411004, India, e-mail: manish.agalave@fergusson.edu

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