On the power-commutative kernel of locally nilpotent groups.
On variants of a theorem of Schur.
Permutability of centre-by-finite groups
Let be a group and be an integer greater than or equal to . is said to be -permutable if every product of elements can be reordered at least in one way. We prove that, if has a centre of finite index , then is -permutable. More bounds are given on the least such that is -permutable.
Powers of a product of commutators as products of squares.
Powers of commutators as products of squares.
Quelques bases et familles basiques des algèbres de Lie libres commodes pour les calculs sur ordinateurs
Reduced Forms for Quadratic Words and Spines of 2-manifolds.
Relative commutator associated with varieties of -nilpotent and of -solvable groups
In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of -nilpotent groups and of -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.
Some conditions implying that an infinite group is abelian
Some conditions on infinite subsets of infinite groups.
Some group theoretic problems inspired by ring theoretic analogies.
Su di un problema combinatorio in teoria dei gruppi
Let be a group and an integer . We say that has the -permutation property if, for any elements in , there exists some permutation of , such that . We prouve that every group is an FC-nilpotent group of class , and that a finitely generated group has the -permutation property (for some ) if, and only if, it is abelian by finite. We prouve also that a group if, and only if, its derived subgroup has order at most 2.
Subgroups of Finite Index in Profinite Groups.
The classification of groups in which every product of four elements can be reordered
The Engel length of the product of Engel elements.
The equation in partially commutative groups.
The equation in partially commutative groups.
The genus problem for one-relator products of locally indicable groups.
The lower central series of the free partially commutative group.
The Ore conjecture
The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.