11 citations · 41 across the 31 of their papers we have counts for
17 papers · 1 filter
Finite groups with two Chermak-Delgado measures
Marius Tărnăuceanu
In this note, we study the finite groups whose Chermak-Delgado measure has exactly two values. They determine an interesting class of -groups containing cyclic groups of prime o…
An -lattice structure associated to some classes of finite groups
Marius Tărnăuceanu
In the present paper we introduce and study a canonical -lattice structure on the set of element orders of some finite groups. We show that a finite abelian group is uniq…
On isomorphisms of canonical -lattices
Marius Tărnăuceanu
The aim of the present paper is to study isomorphisms of canonical -lattices. Some interesting results are obtained in the particular case of isomorphisms between two sub…
An arithmetic method of counting the subgroups of a finite abelian group
Marius Tărnăuceanu
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
A characterization of generalized quaternion 2-groups
Marius Tărnăuceanu
The goal of this note is to give a characterization of generalized quaternion -groups by using their posets of cyclic subgroups.
Addendum to "Subgroup commutativity degrees of finite groups"
Marius Tărnăuceanu
We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.
A note on subgroup coverings of finite groups
Marius Tărnăuceanu
In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as t…
On the total number of principal series of a finite abelian group
Lucian Bentea, Marius Tărnăuceanu
In this note we give a bijective proof for the explicit formula giving the total number of principal series of the direct product …
A note on the product of element orders of finite abelian groups
Marius Tărnăuceanu
Given a finite group , we denote by the product of element orders of . Our main result proves that the restriction of to abelian -groups of order is…
A note on fundamental group lattices
Marius Tărnăuceanu
The main goal of this note is to provide a new proof of a classical result about projectivities between finite abelian groups. It is based on the concept of fundamental group latti…
Finite groups determined by an inequality of the orders of their elements
Marius Tărnăuceanu
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finit…
A note on the number of cyclic subgroups of a finite group
Marius Tărnăuceanu, Mihai-Silviu Lazorec
Let be a finite group, be its poset of cyclic subgroups and consider the quantity . The aim of this paper is to study the class of…
Breaking points in centralizer lattices
Marius Tărnăuceanu
In this note, we prove that the centralizer lattice of a group cannot be written as a union of two proper intervals. In particular, it follows that ${\mathfr…
A nilpotency criterion for finite groups
Marius Tărnăuceanu
Let be a finite group. In this short note, we give a criterion of nilpotency of based on the existence of elements of certain order in each section of .
A note on subgroup commutativity degrees of finite groups
Marius Tărnăuceanu
In this note we give some new results concerning the subgroup commutativity degree of a finite group . These are obtained by considering the minimum of subgroup commutativity de…
A note on a class of gyrogroups
Marius Tărnăuceanu
In \cite{1}, a class of gyrogroups has been associated to certain groups . We give a necessary and sufficient condition for to be gyrocommutative…
Finite groups with two relative subgroup commutativity degrees
Mihai-Silviu Lazorec, Marius Tărnăuceanu
In this paper we show that there is an infinite number of finite groups with two relative subgroup commutativity degrees. Also, we indicate a sufficient condition such that a finit…