On Posets of Classes of Subgroups with Same Set of Orders of Elements
Group Theory
2026-03-09 v1
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.
Cite
@article{arxiv.2603.06179,
title = {On Posets of Classes of Subgroups with Same Set of Orders of Elements},
author = {Sachin Ballal and Tushar Halder},
journal= {arXiv preprint arXiv:2603.06179},
year = {2026}
}
Comments
19 pages, 3 figures