M. Tărnăuceanu

collaborators

9 papers

math.GR2026

On a divisibility condition related to the sum of element orders of a finite group

Marius Tărnăuceanu

Given a finite group $G$ , we denote by $ψ (G)$ the sum of element orders of $G$ . In this note, we determine finite groups $G$ such that $∣ H ∣ - ∣ K ∣$ divides $ψ (H) - ψ (K)$ for all subgrou…

math.GR2026

Two new functions related to the sum of element orders of a finite group

Marius Tărnăuceanu

Let $G$ be a finite group and $H$ be a proper normal subgroup of $G$ . In this note, we introduce two new functions $o (G, H)$ and $ψ^{''} (G, H)$ involving the sums of element orders of $…

math.GR2025

The Reidemeister spectrum of ZM-groups

Marius TÄrnÄuceanu

Given a group $G$ and an automorphism $I ¨ $ of $G$ , two elements $x, y \in G$ are said to be $I ¨ $ -conjugate if $x = g y I ¨ (g)^{- 1}$ for some $g \in G$ . The number $R (I ¨ )$ of equivalence cl…

math.GR2025

On the number of conjugacy classes of subgroups of a finite group

Mihai-Silviu Lazorec, Marius TÄrnÄuceanu, Marius Tărnăuceanu

Let $k^{'} (G)$ and $L (G)$ be the number of conjugacy classes of subgroups and the subgroup lattice of a finite group $G$ , respectively. Our objective is to study some aspects related…

math.GR2025

Almost and quasi Leinster groups

Iulia-CÄtÄlina PleÅca, Marius TÄrnÄuceanu

In this paper, we study the parallelism between perfect numbers and Leinster groups and continue it by introducing the new concepts of almost and quasi Leinster groups which parall…

math.GR2025

A result on certain sums of element orders in finite groups

Marius TÄrnÄuceanu

Given a finite group $G$ of order $p^{n} m$ , where $p$ is a prime and $p ∤ m$ , we denote by $I ¨ _{p} (G)$ the sum of orders of $p$ -parts of elements in $G$ . In the current note, we pro…