It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky’s hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid can be represented by a context-sensitive language but, in general, it cannot be represented by a context-free language.

An endomorphism φ of a free group is called primitivity preserving if φ takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank n ≥ 3 is an automorphism.

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group Z0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z.

that is both analytic (as a mapping of complex manifolds) and algebraic: addition of points in E(C) corresponds to addition in C modulo the lattice L. This correspondence between lattices and elliptic curves over C is known as the Uniformization Theorem; we will spend this lecture and part of the next proving it. To make the correspondence explicit, we need to specify the map Φ from C/L and an ...

Endomorphism algebras gure prominently in group representation theory. F or example, if G is a nite group of Lie type, the representation theory of the endomorphism algebra End G Cj G B |sometimes known as the Hecke algebra over C of G|plays a central role in unraveling the complex unipotent c haracters on G 22, 77. Another example arises in the modular representation theory of the nite general...

Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of th...