A special case of the main result is the following. Let G be a finite, non-supersoluble group in
which from arbitrary subsets X, Y of cardinality n we can always find x∈ X and y∈ Y …

The purpose of this paper is to present a comprehensive overview of known results on
certain combinatorial problems which are related to infinite subsets of a group. Moreover, in …

A note on Torsion-by-Nilpotent Groups. Page 1 REND. SEM. MAT. UNIV. PADOVA, Vol. 117
2007) A note on Torsion-by-Nilpotent Groups. TAREK ROUABHI *) - NADIR TRABELSI **) …

The main result of this note is that a finitely generated hyper-(Abelian-byfinite) group G is
finite-by-nilpotent if and only if every infinite subset contains two distinct elements x, y such …

Let k> 0 an integer. F, τ, N, Nk, and A denote, respectively, the classes of finite, torsion,
nilpotent, nilpotent of class at most k, group in which every two generator subgroup is in Nk …

Let k> 0 an integer. F, τ, N, Nk, N(2) k and A denote the classes of finite, torsion, nilpotent,
nilpotent of class at most k, group which every two generator subgroup is Nk and abelian …

Abstract Let\(k> 0\) an integer.\(F\),\(\tau\),\(N\),\(N_ {k}\),\(N_ {k}^{(2)}\) and\(A\) denote the
classes of finite, torsion, nilpotent, nilpotent of class at most\(k\), group which every two …

Let F, N, A and N 2 denote the properties of being finite, nilpotent, abelian and nilpotent of
classes at most 2, respectively. Firstly we consider the class of finitely generated FN-groups …

Let k> 0 an integer. F nilpotent, nilpotent of class at m groups. The main results of this p
property FC is closed under finit class ((τNk) τ,∞)(respectively ((τ deduce that a finitely …