15 citations · 53 across the 33 of their papers we have counts for
8 papers · 1 filter
On a conjecture by Haipeng Qu
Marius Tărnăuceanu
In this note, we prove that is the non-elementary abelian -group of order , , whose number of subgroups of possible orders is maximal. This s…
The number of cyclic subgroups of finite abelian groups and Menon's identity
Marius Tărnăuceanu
In this note, we give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on applying the Burnside's lemma to a certain group action. Also, it…
Solitary quotients of finite groups
Marius Tărnăuceanu
In this paper we introduce and study the lattice of normal subgroups of a group that determine solitary quotients. It is closely connected to the well-known lattice of solitary…
On the sum of element orders of finite abelian groups
Marius Tărnăuceanu, Dan Gregorian Fodor
In this note some properties of the sum of element orders of a finite abelian group are studied.
Finite groups determined by an inequality of the orders of their normal subgroups
Marius Tărnăuceanu
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known ar…
Minimal non-Iwasawa finite groups
Marius Tărnăuceanu
In this note, we describe first the structure of minimal non-Iwasawa finite groups. Then we determine the minimal non-Iwasawa finite groups which are modular. Also, we find connect…