Numbers which are only orders of abelian or nilpotent groups

2021/02/01 by Matthew Just, Just, Matthew
Mathematics · #Functional Equations Stability Results #Advanced Mathematical Identities #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2102.01027

Abstract

Refining a result of Erdos and Mays, we give asymptotic series expansions for the functions A(x)-C(x), the count of n≤ x for which every group of order n is abelian (but not all cyclic), and N(x)-A(x), the count of n≤ x for which every group of order n is nilpotent (but not all abelian).

Related

• Numbers which are orders only of cyclic groups
• On some sums involving the counting function of non-isomorphic abelian groups
• Counting nilpotent Galois extensions
• On the characterization of the numbers n such that any group of order n has a given property P
• Arithmétique des Groupes Abéliens Finis