Infinite iteration of matrix semigroups. I: Structure theorem for torsion semigroups
The main result of this paper is a representation theorem for countable torsion monoids, that is, countable monoids in which every element is of finite order. Every such monoid T is the homomorphic image \(\sigma\) (S) of a torsion monoid S with S and \(\sigma\) having several special properties some of which can be roughly described as follows: S is obtained by an infinitely iterated sandwich matrix type of construction based on certain cyclic submonoids of T and on translations of finite subsets of T. The morphism \(\sigma\) is of a restricted kind, defined along with the matrix construction. The maximal subgroups of S are finite cyclic groups and the restriction of \(\sigma\) to these is injective. S can be characterized as an elementary projective limit of finitely iterated matrix semigroups.
projective limit of finitely iterated matrix semigroups
scientific article; zbMATH DE number 3935334