On Posets of Classes of Automorphic Subgroups of Finite Groups

2025/11/01 by Sachin Ballal, Ballal, Sachin, Halder, Tushar
Mathematics · Decision Sciences · #Finite Group Theory Research #Rings, Modules, and Algebras #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2511.00433

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 §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.

Citations

• The posets of classes of isomorphic subgroups of finite groups

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