M. Herzog

activity

20102023

most citedA new solvability criterion for finite groups

17 citations · 31 across the 9 of their papers we have counts for

collaborators

12 papers

math.GR2023

On conjygacy classes in groups

Marcel Herzog, Patrizia Longobardi, Mercede Maj

Let $G$ be a group. Write $G^{*} = G ∖ {1}$ . An element $x$ of $G^{*}$ will be called deficient if $⟨ x ⟩ < C_{G} (x)$ and it will be called non-deficient if $\lang…

math.GR2022

On groups in which every element has a prime power order and which satisfy some boundedness condition

Marcel Herzog, Patrizia Longobardi, Mercede Maj

In this paper we shall deal with periodic groups, in which each element has a prime power order. A group $G$ will be called a $B C P$ -group if each element of $G$ has a prime power o…

math.GR2019

Sums of element orders in groups of odd order

Marcel Herzog, Patrizia Longobardi, Mercede Maj

Denote by $G$ a finite group and by $ψ (G)$ the sum of element orders in $G$ . If $t$ is a positive integer, denote by $C_{t}$ the cyclic group of order $t$ and write $ψ (t) = ψ (C_{t})$ . In…

math.GR2019

The second maximal groups with respect to the sum of element orders

Marcel Herzog, Patrizia Longobardi, Mercede Maj

Denote by $G$ a finite group and let $ψ (G)$ denote the sum of element orders in $G$ . In 2009, H.Amiri, S.M.Jafarian Amiri and I.M.Isaacs proved that if $∣ G ∣ = n$ and $G$ is non-cycli…

math.GR2016

An exact upper bound for sums of element orders in non-cyclic finite groups

Marcel Herzog, Patrizia Longobardi, Mercede Maj

Denote the sum of element orders in a finite group $G$ by $ψ (G)$ and let $C_{n}$ denote the cyclic group of order $n$ . Suppose that $G$ is a non-cyclic finite group of order $n$ and…

math.NT2016★ 2 cited

Small doubling in ordered nilpotent groups of class 2

Gregory A. Freiman, Marcel Herzog, Patrizia Longobardi +2

The aim of this paper is to present a complete description of the structure of finite subsets with small doubling property in ordered nilpotent groups of class 2.

math.GR2016

Finite groups with non-trivial intersections of kernels of all but one irreducible characters

Mariagrazia Bianchi, Marcel Herzog

In this paper we consider finite groups G satisfying the following condition: G has two columns in its character table which differ by exactly one entry. It turns out that such gro…

math.GR2015★ 8 cited

On the structure of subsets of an orderable group with some small doubling properties

G. A. Freiman, M. Herzog, P. Longobardi +4

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and <S> is non-abelian.

math.NT2015★ 3 cited

Small doubling in ordered groups: generators and structure

Gregory A. Freiman, Marcel Herzog, Patrizia Longobardi +3

We prove several new results on the structure of the subgroup generated by a small doubling subset of an ordered group, abelian or not. We obtain precise results generalizing Freim…

math.GR2013

Conjugacy classes of finite groups and graph regularity

Mariagrazia Bianchi, Rachel D. Camina, Marcel Herzog +1

Given a finite group $G$ , denote by $Γ (G)$ the simple undirected graph whose vertices are the distinct sizes of noncentral conjugacy classes of $G$ , and set two vertices of $Γ (G)$ …

math.GR2011★ 17 cited

A new solvability criterion for finite groups

Silvio Dolfi, Robert Guralnick, Marcel Herzog +1

In 1968, John Thompson proved that a finite group G is solvable if and only if every 2-generator subgroup of G is solvable. In this paper, we prove that solvability of a finite gro…

math.GR2010★ 1 cited

A new solvability criterion for finite groups

Silvio Dolfi, Marcel Herzog, Cheryl E. Praeger

In 1968, John Thompson proved that a finite group $G$ is solvable if and only if every $2$ -generator subgroup of $G$ is solvable. In this paper, we prove that solvability of a fini…