Marcel Herzog

activity

20102023

most citedA new solvability criterion for finite groups

1 citations · 2 across the 4 of their papers we have counts for

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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.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.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…