In this paper we continue our study on 4-Engel groups. Before we discuss the contents of the paper we give a short overview on what is known on 4-Engel groups. The main open question concerning their… (More)

This paper begins the development of a theory of what we will call symplectic alternating algebras. They have arisen in the study of 2-Engel groups but seem also to be of interest in their own right.… (More)

Recently Havas and Vaughan-Lee proved that 4-Engel groups are locally nilpotent. Their proof relies on the fact that a certain 4-Engel group T is nilpotent and this they prove using a computer and… (More)

Let G be a finite group. We consider the set of the irreducible complex characters of G, namely Irr(G), and the related degree set cd(G) = {χ(1) : χ ∈ Irr(G)}. Let ρ(G) be the set of all primes which… (More)

We obtain an explicit bound for the nilpotency class of n-Engel Lie algebras of characteristic zero. 1991 Mathematics Subject Classification (Amer. Math. Soc.): 17B30.

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is… (More)

Let Be be the variety of groups of exponent dividing e andNc the variety of nilpotent groups of class at most c. In addition, we denote by A = N1 the variety of abelian groups and by Ap = A ∩ Bp the… (More)

In this paper we continue developing the theory of symplectic alternating algebras that was started in [3]. We focus on nilpotency, solubility and nil-algebras. We show in particular that symplectic… (More)