ON THE SUM OF INVERSES OF SUBGROUP ORDERS IN FINITE GROUPS

MARIUS TĂRNĂUCEANU

Faculty of Mathematics “Al.I. Cuza" University, Iași, ROMANIA
e-mail: tarnauc@uaic.ro

Abstract

Let G be a finite group and $f(G)=\sum_{H\leq G}\frac{1}{|H|}$\, i.e. let f(G) be the sum of inverses of the orders of all subgroups H of G. In this note, we study the finite groups G such that f(G) is no greater than 2.

Keywords

finite groups ZM-groups subgroup orders.