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arXiv · 2511.00433

On Posets of Classes of Automorphic Subgroups of Finite Groups

Sachin Ballal·Tushar Halder
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Abstract

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 {\S}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.

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Sachin Ballal, Tushar Halder. 2025-11-01. On Posets of Classes of Automorphic Subgroups of Finite Groups. https://arxiv.org/abs/2511.00433

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