8 citations · 13 across the 9 of their papers we have counts for
11 papers
Limit Groups and Automorphisms of -Existentially Closed Groups
Burak Kaya, Mahmut Kuzucuoğlu, Patrizia Longobardi +1
The structure of automorphism groups of -existentially closed groups are studied by Kaya-Kuzucuoğlu in 2022. It was proved that Aut(G) is the union of subgroups of level preserv…
Left -Engel elements in groups: A survey
Anastasia Hadjievangelou, Patrizia Longobardi, Mercede Maj +3
We survey left 3-Engel elements in groups.
On conjygacy classes in groups
Marcel Herzog, Patrizia Longobardi, Mercede Maj
Let be a group. Write . An element of will be called deficient if and it will be called non-deficient if $\lang…
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 will be called a -group if each element of has a prime power o…
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…
Sums of element orders in groups of odd order
Marcel Herzog, Patrizia Longobardi, Mercede Maj
Denote by a finite group and by the sum of element orders in . If is a positive integer, denote by the cyclic group of order and write . In…
The second maximal groups with respect to the sum of element orders
Marcel Herzog, Patrizia Longobardi, Mercede Maj
Denote by a finite group and let denote the sum of element orders in . In 2009, H.Amiri, S.M.Jafarian Amiri and I.M.Isaacs proved that if and is non-cycli…
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 by and let denote the cyclic group of order . Suppose that is a non-cyclic finite group of order and…
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.
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.
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…