Marius Tùarnùauceanu

activity

20122022

most citedAn inequality detecting nilpotency of finite groups

3 citations · 5 across the 8 of their papers we have counts for

collaborators

35 papers

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

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

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…