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.
The structure of the rings assigned to group varieties
The width of a power of a free nilpotent group of nilpotency class 2.
The Zassenhaus decomposition for the orthogonal group: properties and applications.