Marius Tùarnùauceanu

activity

20122025

most citedAn arithmetic method of counting the subgroups of a finite abelian group

11 citations · 41 across the 31 of their papers we have counts for

collaborators

43 papers

math.GR2025

Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups

Marius Tărnăuceanu

In this paper, we count the number of conjugacy and automorphism-conjugacy classes of elements of a ZM-group. The size of a conjugacy class with respect to these two equivalence re…

math.GR2024

Finite groups with dense solitary subgroups

Marius Tărnăuceanu

A group $G$ is said to have dense solitary subgroups if each non-empty open interval in its subgroup lattice $L (G)$ contains a solitary subgroup. In this short note, we find all fi…

math.GR2023

A characterization of $A_{5}$ by its average order

Marius Tărnăuceanu

Let $o (G)$ be the average order of a finite group $G$ . M. Herzog, P. Longobardi and M. Maj \cite{7} showed that if $G$ is non-solvable and $o (G) = o (A_{5})$ , then $G ≅ A_{5}$ . In this…

math.GR2022

On the average order of a finite group

Mihai-Silviu Lazorec, Marius Tărnăuceanu

Let $o (G)$ be the average order of a finite group $G$ . We show that if $o (G) < c$ , where $c \in {\frac{13}{6}, \frac{11}{4}}$ , then $G$ is an elementary abelian 2-group o…

math.GR2022★ 7 cited

Finite groups with large Chermak-Delgado lattices

Georgiana Fasolă, Marius Tărnăuceanu

Given a finite group $G$ , we denote by $L (G)$ the subgroup lattice of $G$ and by $C D (G)$ the Chermak-Delgado lattice of $G$ . In this note, we determine the finite groups $G$ …

math.GR2022

Another criterion for supersolvability of finite groups

Marius Tărnăuceanu

Let $o (G)$ be the average order of a finite group $G$ . In this paper, we prove that if $o (G) < \frac{31}{12}$ \,, then $G$ is supersolvable. Moreover, we have $o (G) = \frac{31}{12}$ if…

math.GR2021

Finite groups with many isolated subgroups

Marius Tărnăuceanu

Given a finite group $G$ , we denote by $L (G)$ the subgroup lattice of $G$ and by $Isolated (G)$ the set of isolated subgroups of $G$ . In this note, we describe finite groups $…

math.GR2021

Generalizing the Lehmer's totient problem

Marius Tărnăuceanu

An important unsolved question in number theory is the Lehmer's totient problem that asks whether there exists any composite number $n$ such that $φ (n) ∣ n - 1$ , where $φ$ is the E…

math.GR2021★ 2 cited

A new Menon-type identity derived from group actions

Marius Tărnăuceanu

In this short note, we give a new Menon-type identity involving the sum of element orders and the sum of cyclic subgroup orders of a finite group. It is based on applying the weigh…

math.GR2021

On the supersolvability of a finite group by the sum of subgroup orders

Marius Tărnăuceanu

Let $G$ be a finite group and $σ_{1} (G) = \frac{1}{∣ G ∣} \sum_{H \leq G} ∣ H ∣$ . In this paper, we prove that if $σ_{1} (G) < 2 + \frac{11}{∣ G ∣}$ \,, then $G$ is supersolvable. In particular, some…

math.GR2021

Isolated subgroups of finite abelian groups

Marius Tărnăuceanu

We say that a subgroup $H$ is isolated in a group $G$ if for every $x \in G$ we have either $x \in H$ or $⟨ x ⟩ \cap H = 1$ . In this short note, we describe the set of isolat…

math.GR2020

Arithmetic progressions in finite groups

Marius Tărnăuceanu

In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r \geq 2$ . This extends t…

math.GR2020

A result on the number of cyclic subgroups of a finite group

Marius Tărnăuceanu

Let $G$ be a finite group and $α (G) = \frac{∣ C ( G ) ∣}{∣ G ∣}$ \,, where $C (G)$ denotes the set of cyclic subgroups of $G$ . In this short note, we prove that $α (G) \leq α (Z (G))$ and we descr…

math.GR2020

A generalization of a result on the sum of element orders of a finite group

Marius Tărnăuceanu

Let $G$ be a finite group and let $ψ (G)$ denote the sum of element orders of $G$ . It is well-known that the maximum value of $φ$ on the set of groups of order $n$ , where $n$ is a p…

math.GR2019

How large a union of proper subgroups of a finite group can be?

Marius Tărnăuceanu

Let $k$ be a positive integer and $G$ be a finite group that cannot be written as the union of $k$ proper subgroups. In this short note, we study the existence of a constant $c_k\i…

math.GR2019★ 2 cited

A criterion for solvability of a finite group by the sum of subgroup orders

Marius Tărnăuceanu

Let $G$ be a finite group and $σ_{1} (G) = \frac{1}{∣ G ∣} \sum_{H \leq G} ∣ H ∣$ . In this note, we prove that if $σ_{1} (G) < \frac{117}{20}$ , then $G$ is solvable. Moreover, we have $σ_1(G)=\fr…

math.GR2019

Detecting structural properties of finite groups by the sum of element orders

Marius Tărnăuceanu

In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpote…

math.GR2019

A criterion for nilpotency of a finite group by the sum of element orders

Marius Tărnăuceanu

Denote the sum of element orders in a finite group $G$ by $ψ (G)$ and let $C_{n}$ denote the cyclic group of order $n$ . In this paper, we prove that if $∣ G ∣ = n$ and $ψ(G)>\frac{13}{21}…

math.GR2018

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 $p$ -groups containing cyclic groups of prime o…

math.GR2018

An $E$ -lattice structure associated to some classes of finite groups

Marius Tărnăuceanu

In the present paper we introduce and study a canonical $E$ -lattice structure on the set of element orders of some finite groups. We show that a finite abelian group is uniq…

math.GR2018

On isomorphisms of canonical $E$ -lattices

Marius Tărnăuceanu

The aim of the present paper is to study isomorphisms of canonical $E$ -lattices. Some interesting results are obtained in the particular case of isomorphisms between two sub…

math.GR2018★ 11 cited

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.

math.GR2018

A characterization of generalized quaternion 2-groups

Marius Tărnăuceanu

The goal of this note is to give a characterization of generalized quaternion $2$ -groups by using their posets of cyclic subgroups.

math.GR2018

Addendum to "Subgroup commutativity degrees of finite groups" $[J. Algebra 321 (2009), 2508-2520]$

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.

Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups

Finite groups with dense solitary subgroups

A characterization of A5​ by its average order

On the average order of a finite group

Finite groups with large Chermak-Delgado lattices

Another criterion for supersolvability of finite groups

Finite groups with many isolated subgroups

Generalizing the Lehmer's totient problem

A new Menon-type identity derived from group actions

On the supersolvability of a finite group by the sum of subgroup orders

Isolated subgroups of finite abelian groups

Arithmetic progressions in finite groups

A result on the number of cyclic subgroups of a finite group

A generalization of a result on the sum of element orders of a finite group

How large a union of proper subgroups of a finite group can be?

A criterion for solvability of a finite group by the sum of subgroup orders

Detecting structural properties of finite groups by the sum of element orders

A criterion for nilpotency of a finite group by the sum of element orders

Finite groups with two Chermak-Delgado measures

An E-lattice structure associated to some classes of finite groups

On isomorphisms of canonical E-lattices

An arithmetic method of counting the subgroups of a finite abelian group

A characterization of generalized quaternion 2-groups

Addendum to "Subgroup commutativity degrees of finite groups" [J. Algebra 321 (2009), 2508-2520]

A characterization of $A_{5}$ by its average order

An $E$ -lattice structure associated to some classes of finite groups

On isomorphisms of canonical $E$ -lattices

Addendum to "Subgroup commutativity degrees of finite groups" $[J. Algebra 321 (2009), 2508-2520]$