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

Showing 2021Show all

5 papers · 1 filter

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…