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 2019Show all

4 papers · 1 filter

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}…