M. Herzog

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20162022

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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

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…