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arXiv · 2603.06179

On Posets of Classes of Subgroups with Same Set of Orders of Elements

Sachin Ballal·Tushar Halder
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Abstract

In this paper, we study the posets of classes of subgroups of finite group having same set of orders of elements. We show that this poset is a chain only in the case of p-groups and moreover, we characterize all finite groups for which this poset is C2, the chain with two elements. We also show that this poset forms a lattice in the case of finite cyclic and dihedral groups and give a characterization when this lattice is distributive and modular.

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Sachin Ballal, Tushar Halder. 2026-03-06. On Posets of Classes of Subgroups with Same Set of Orders of Elements. https://arxiv.org/abs/2603.06179

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