In the context of self-studies on polynomials of degree 5 (quintics), Galois groups and field extensions related to solvable quintics - irreducible and reducible ones - have been analyzed. Effort has been spent to provide comprehensive explanations and some examples of those structures; the intention is to give the reader an overview and a decent insight into the topic, which may help to understand the algebraic structures and their arithmetics better.

Achim Plum holds a degree (Diplom) from RWTH Aachen, Germany, in Computer Science with Mathematics as second discipline. For a long time, he worked in different industries as a professional in Information Technology and Management. Beyond this, he stayed interested in mathematical topics and keeps studying further in Mathematics and related areas.