M. Tărnăuceanu

activity

20152021

most citedTwo classes of finite groups whose Chermak-Delgado lattice is a chain of length zero

10 citations · 10 across the 6 of their papers we have counts for

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20 papers · 1 filter

math.GR2021

On a group-theoretical generalization of the Euler's totient function

Marius Tărnăuceanu

Let $G$ be a finite group and $φ (G) = ∣ {a \in G ∣ o (a) = exp (G)} ∣$ , where $o (a)$ denotes the order of $a$ in $G$ and $exp (G)$ denotes the exponent of $G$ . Under a natural hypothe…

math.GR2020

Groups whose same-order types are arithmetic progressions

Mihai-Silviu Lazorec, Marius Tarnauceanu

The same-order type $τ_{e} (G)$ of a finite group $G$ is a set formed of the sizes of the equivalence classes containing the same order elements of $G$ . In this paper, we study an ari…

math.GR2020

The second minimum/maximum value of the number of cyclic subgroups of finite $p$ -groups

Mihai-Silviu Lazorec, Rulin Shen, Marius Tărnăuceanu

Let $C (G)$ be the poset of cyclic subgroups of a finite group $G$ and let $P$ be the class of $p$ -groups of order $p^{n}$ ( $n \geq 3$ ). Consider the function $α:\mathcal{P}\…

math.GR2019

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

Mihai-Silviu Lazorec, Tărnăuceanu Marius

Let $G$ be the class of all finite groups and consider the function $ψ^{''} : G ⟶ (0, 1]$ , given by $ψ^{''} (G) = \frac{ψ ( G )}{∣ G ∣ ^{2}}$ , where $ψ (G)$ is the sum o…

math.GR2018

On a conjecture by Haipeng Qu

Marius Tărnăuceanu

In this note, we prove that $D_{8} \times C_{2}^{n - 3}$ is the non-elementary abelian $2$ -group of order $2^{n}$ , $n \geq 3$ , whose number of subgroups of possible orders is maximal. This s…

math.GR2018

The number of cyclic subgroups of finite abelian groups and Menon's identity

Marius Tărnăuceanu

In this note, we give a new formula for the number of cyclic subgroups of a finite abelian group. This is based on applying the Burnside's lemma to a certain group action. Also, it…

On a group-theoretical generalization of the Euler's totient function

Groups whose same-order types are arithmetic progressions

The second minimum/maximum value of the number of cyclic subgroups of finite p-groups

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

On a conjecture by Haipeng Qu

The number of cyclic subgroups of finite abelian groups and Menon's identity

The second minimum/maximum value of the number of cyclic subgroups of finite $p$ -groups