P. Longobardi

activity

20192022

collaborators

4 papers

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.GR2020

On the structure of some locally nilpotent groups without contranormal subgroups

Leonid A. Kurdachenko, Patrizia Longobardi, Mercede MAJ

Following J.S. Rose, a subgroup H of a group G is said contranormal in G if G = H^G . In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well kn…

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…