Mihai-Silviu Lazorec

activity

20162026

most citedA note on the number of cyclic subgroups of a finite group

3 citations · 8 across the 15 of their papers we have counts for

collaborators

23 papers

math.GR2026

A set theoretic version of equations on groups

Mihai-Silviu Lazorec

Let $G$ be a finite group. The aim of this paper is to study the number of solutions $S \subseteq G$ of the equation $℧^{{n}} (S) = L$ , where $L$ is a non-empty subset of $G$ , $n$ …

math.GR2026

On some problems regarding $L C M$ -groups

Mihai-Silviu Lazorec

Let $G$ be a finite group and denote by $o (g)$ the order of an element $g \in G$ . We say that $G$ is an $L C M$ -group if $o (x^{n} y)$ is a divisor of the least common multiple of $o(x^n)…

math.GR2026

Minimum $F$ -covers: the supersolvable and metabelian cases

Mihai-Silviu Lazorec

Given a set $F$ of finite groups, it is said that a group $G$ is an $F$ -cover if every group in $F$ is isomorphic to a subgroup of $G$ . Moreover, $G$ …

math.GR2025

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

Mihai-Silviu Lazorec, 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.GR2024

On two problems about order sequences of finite groups

Mihai-Silviu Lazorec

The order sequence of a finite group $G$ is a non-decreasing finite sequence formed of the element orders of $G$ . Several properties of order sequences were studied by P. J. Camero…

math.GR2024

Element orders in extraspecial groups

Mihai-Silviu Lazorec

By using the structure and some properties of extraspecial and generalized/almost extraspecial $p$ -groups, we explicitly determine the number of elements of specific orders in such…

math.GR2024★ 2 cited

Subgroups with a small sum of element orders

Mihai-Silviu Lazorec

A finite group $G$ is said to be a $B_{ψ}$ -group if $ψ (H) < ∣ G ∣$ for any proper subgroup $H$ of $G$ , where $ψ (H)$ denotes the sum of element orders of $H$ . In this paper, we…

math.GR2023

Some density results involving the average order of a finite group

Mihai-Silviu Lazorec

Let $o (G)$ be the average of the element orders of a finite group $G$ . A research topic concerning this quantity is understanding the relation between $o (G)$ and $o (H)$ , where $H$ …

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

A graph related to the sum of element orders of a finite group

Mihai-Silviu Lazorec

A finite group is called $ψ$ -divisible iff $ψ (H) ∣ ψ (G)$ for any subgroup $H$ of a finite group $G$ . Here, $ψ (G)$ is the sum of element orders of $G$ . For now, the only known example…

math.GR2021

Addendum to "A generalization of a result on the sum of element orders of a finite group" [arXiv:2001.07275]

Mihai-Silviu Lazorec, Marius Tărnăuceanu

Let $G$ be a group of order $n$ and $H$ be a subgroup of order $m$ of $G$ . Denote by $ψ_{H} (G)$ the sum of element orders relative to $H$ of $G$ . It is known that if $G$ is nilpotent…

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

On a divisibility property involving the sum of element orders

Mihai-Silviu Lazorec

A finite group $G$ is called $ψ$ -divisible if $ψ (H) ∣ ψ (G)$ for any subgroup $H$ of $G$ , where $ψ (H)$ and $ψ (G)$ are the sum of element orders of $H$ and $G$ , respectively. In this p…

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.GR2019

A connection between the number of subgroups and the order of a finite group

Mihai-Silviu Lazorec

For a finite group $G$ , we associate the quantity $β (G) = \frac{∣ L ( G ) ∣}{∣ G ∣}$ , where $L (G)$ is the subgroup lattice of $G$ . Different properties and problems related to this ratio ar…

math.GR2018★ 3 cited

A note on the number of cyclic subgroups of a finite group

Marius Tărnăuceanu, Mihai-Silviu Lazorec

Let $G$ be a finite group, $L_{1} (G)$ be its poset of cyclic subgroups and consider the quantity $α (G) = \frac{∣ L _{1} ( G ) ∣}{∣ G ∣}$ . The aim of this paper is to study the class $C$ of…

math.GR2018

Relative cyclic subgroup commutativity degrees of finite groups

Mihai-Silviu Lazorec

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in…

math.GR2018

Finite groups with two relative subgroup commutativity degrees

Mihai-Silviu Lazorec, Marius Tărnăuceanu

In this paper we show that there is an infinite number of finite groups with two relative subgroup commutativity degrees. Also, we indicate a sufficient condition such that a finit…

math.GR2017

Probabilistic aspects of ZM-groups

Mihai-Silviu Lazorec

In this paper we study probabilistic aspects such as (cyclic) subgroup commutativity degree and (cyclic) factorization number of ZM-groups. We show that these quantities can be com…

math.GR2017

Cyclic factorization numbers of finite groups

Marius Tărnăuceanu, Mihai-Silviu Lazorec

In this paper we introduce and study the concept of cyclic factorization number of a finite group G. By using the Mobius inversion formula and other methods involving the cyclic s…

math.GR2016★ 3 cited

On some probabilistic aspects of (generalized) dicyclic groups

Marius Tărnăuceanu, Mihai-Silviu Lazorec

In this paper we study probabilistic aspects such as subgroup commutativity degree and cyclic subgroup commutativity degree of the (generalized) dicyclic groups. We find explicit f…

math.GR2016

Cyclic subgroup commutativity degrees of finite groups

Marius Tarnauceanu, Mihai-Silviu Lazorec

In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$ . This quantity measures the probability of two random cyclic subgroup…

A set theoretic version of equations on groups

On some problems regarding LCM-groups

Minimum F-covers: the supersolvable and metabelian cases

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

On two problems about order sequences of finite groups

Element orders in extraspecial groups

Subgroups with a small sum of element orders

Some density results involving the average order of a finite group

On the average order of a finite group

A graph related to the sum of element orders of a finite group

Addendum to "A generalization of a result on the sum of element orders of a finite group" [arXiv:2001.07275]

Groups whose same-order types are arithmetic progressions

On a divisibility property involving the sum of element orders

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

A connection between the number of subgroups and the order of a finite group

A note on the number of cyclic subgroups of a finite group

Relative cyclic subgroup commutativity degrees of finite groups

Finite groups with two relative subgroup commutativity degrees

Probabilistic aspects of ZM-groups

Cyclic factorization numbers of finite groups

On some probabilistic aspects of (generalized) dicyclic groups

Cyclic subgroup commutativity degrees of finite groups

On some problems regarding $L C M$ -groups

Minimum $F$ -covers: the supersolvable and metabelian cases

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