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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.00433 |
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| _version_ | 1866909881698615296 |
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| author | Ballal, Sachin Halder, Tushar |
| author_facet | Ballal, Sachin Halder, Tushar |
| contents | In [16], Tarnauceanu studied the poset Iso(G), of isomorphic classes of subgroups of a finite group G and proposed several questions for further research. In this paper, we study the poset AutCl(G), of classes of automorphic subgroups of finite group G. We introduce a partial order on AutCl(G) to tackle problem 5 mentioned in §4 of [16]. More precisely, we prove that AutCl(Dn) and AutCl(Q4m) are distributive lattices. Moreover, we characterize all classes of finite groups for which AutCl(G) is a chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Posets of Classes of Automorphic Subgroups of Finite Groups Ballal, Sachin Halder, Tushar Group Theory 06A06, 06B99, 20D30, etc In [16], Tarnauceanu studied the poset Iso(G), of isomorphic classes of subgroups of a finite group G and proposed several questions for further research. In this paper, we study the poset AutCl(G), of classes of automorphic subgroups of finite group G. We introduce a partial order on AutCl(G) to tackle problem 5 mentioned in §4 of [16]. More precisely, we prove that AutCl(Dn) and AutCl(Q4m) are distributive lattices. Moreover, we characterize all classes of finite groups for which AutCl(G) is a chain. |
| title | On Posets of Classes of Automorphic Subgroups of Finite Groups |
| topic | Group Theory 06A06, 06B99, 20D30, etc |
| url | https://arxiv.org/abs/2511.00433 |