On Posets of Classes of Subgroups with Same Set of Orders of Elements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917318304464896 |
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| author | Ballal, Sachin Halder, Tushar |
| author_facet | Ballal, Sachin Halder, Tushar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Posets of Classes of Subgroups with Same Set of Orders of Elements Ballal, Sachin Halder, Tushar Group Theory 06A06, 06B99, 20D30, etc 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. |
| title | On Posets of Classes of Subgroups with Same Set of Orders of Elements |
| topic | Group Theory 06A06, 06B99, 20D30, etc |
| url | https://arxiv.org/abs/2603.06179 |