Topics of entropy in locally compact abelian groups - Waka, Olwethu (Department of Mathematics and Applied Mathematics, 2022)
The present MSc thesis discusses some notions of abelian group theory in connection with recent topics of topological entropy of locally compact abelian groups. It has been used the reference of [D. J. S. Robinson, A Course in the Theory of Groups, Springer, 1996, New York], which is a classical textbook in group theory. A list of exercises, relevant to our purposes, has been selected, in order to introduce some recent aspects of topological entropy of locally compact abelian groups. It is worth to mention that many of the exercises, which have been solved in the present thesis, are subject to technicalities which require the application of theorems of decomposition for abelian groups. Therefore the logic of the solutions allows us to describe the topological entropy in presence of an appropriate factorization.