Automorphisms of a free nilpotent algebra

A Note on Automorphisms of Free Nilpotent Groups

We exhibit normal subgroups of a free nilpotent group F of rank two and class three, which have isomorphic finite quotients but are not conjugate under any automorphism of F . A remarkable fact about free profinite groups of finite rank is that any isomorphism between finite quotients of such a group F lifts to an automorphism of F . This is true, more generally, if F a free pro-Cgroup of finit...

Automorphisms of a Free Associative Algebra of Rank 2. I

Let Ä<2> = R that keeps (xy — yx) fixed (up to multiplication by an element of R), then . This follows from a more general result about endomorphisms of Ä...

On the Nilpotent Multiplier of a Free Product

Anosov Automorphisms of Nilpotent Lie Algebras

Each matrix A in GLn(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra fn,r. We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.

Subgroups defining automorphisms in locally nilpotent groups

We investigate some situation in which automorphisms of a groupG are uniquely determined by their restrictions to a proper subgroup H . Much of the paper is devoted to studying under which additional hypotheses this property forces G to be nilpotent if H is. As an application we prove that certain countably infinite locally nilpotent groups have uncountably many (outer) automorphisms.