Related papers: Endomorphisms of nilpotent groups of finite rank

We describe inertial endomorphisms of an abelian group $A$, that is endomorphisms $\varphi$ with the property $|(\varphi(X)+X)/X|<\infty$ for each $X\le A$. They form a ring containing multiplications, the so-called finitary endomorphisms…

It is proved that centrally essential rings, whose additive groups of finite rank are torsion-free groups of finite rank, are quasi-invariant but not necessarily invariant. Torsion-free Abelian groups of finite rank with centrally essential…

In this paper we find a necessary and sufficient condition for a finite nilpotent group to have an abelian central automorphism group.

A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…

The isomorphism and quasi-isomorphism relations on the $p$-local torsion-free abelian groups of rank $n\geq3$ are incomparable with respect to Borel reducibility.

Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G…

We describe the groups of inner and outer automorphisms of the free metabelian nilpotent Lie algebra of finite rank over a field of characteristic 0. To obtain this result we first describe the groups of inner and continuous outer…

We consider IA-endomorphisms (i.e., Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the well-known characterization of…

We study Abelian groups $A$ with centrally essential endomorphism ring $\text{End}\,A$. If $A$ is a such group which is either a torsion group or a non-reduced group, then the ring $\text{End}\,A$ is commutative. We give examples of Abelian…

It is known that every torsion-free abelian group of finite rank has a maximal completely decomposable summand that is unique up to isomorphism. We show that groups of infinite rank need not have maximal completely decomposable summands,…

We characterize co-Hopfian finitely generated torsion free nilpotent groups in terms of their Lie algebra automorphisms, and construct many examples of such groups.

We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated and we do the same for periodic points. We also describe the…

It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\,\varphi$ is finitely generated for every endomorphism $\varphi$ of $G$ if and only if $G$ is a free product of free abelian groups. The same conditions hold for…

In this paper we determine the torsion free rank of the group of endotrivial modules for any finite group of Lie type, in both defining and non-defining characteristic. On our way to proving this, we classify the maximal rank $2$ elementary…

This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups…

Suppose $G$ is a $\mathcal{T}$-group (finitely generated torsion-free nilpotent) with centralizers outside of the derived subgroup being abelian of rank equal to $\text{rank}(Z_1)+1$. This includes the class of free nilpotent groups…

We study the word length entropy of automorphisms of residually nilpotent groups, and how the entropy of such group automorphisms relates to the entropy of induced automorphisms on various nilpotent quotients. We show that much like the…

We prove that the growth rate of an endomorphism of a finitely generated nilpotent group equals to the growth rate of induced endomorphism on its abelinization, generalizing the corresponding result for an automorphism in [14]. We also…

We construct finitely generated torsion-free solvable groups $G$ that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of $G$ are virtually abelian. In particular all finitely generated…

A celebrated result of J. Thompson says that if a finite group $G$ has a fixed-point-free automorphism of prime order, then $G$ is nilpotent. The main purpose of this note is to extend this result to finite inverse semigroups. An earlier…