2024/08/15 by Sunil K. Chebolu, Keir Lockridge, Chebolu, Sunil K. +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Equations Stability Results #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2408.08195
openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1960, László Fuchs posed the problem of determining which groups G are realizable as the group of units in some ring R. In \citechebolu2022fuchs, we investigated the following variant of Fuchs' problem, for abelian groups: which groups G are realized by a ring R where every group endomorphism of G is induced by a ring endomorphism of R? Such groups are called fully realizable. In this paper, we answer the aforementioned question for several families of nonabelian groups: symmetric, dihedral, quaternion, alternating, and simple groups; almost cyclic p-groups; and groups whose Sylow 2-subgroup is either cyclic or normal and abelian. We construct three infinite families of fully realizable nonabelian groups using iterated semidirect products.