On the number of diamonds in the subgroup lattice of a finite abelian group

Abstract

The main goal of the current paper is to determine the total number of diamonds in the subgroup lattice of a finite abelian group. This counting problem is reduced to finite p-groups. Explicit formulas are obtained in some particular cases.

Keywords

• abelian group
• subgroup lattice
• diamond lattice
• section
• l-free group
• primary 20d30
• secondary 20d60
• 20k27