Basic Aspects in Group Theory. Part 8: Unique Decomposition of Torsion.
This story follows-up and concludes the series about basic aspects in group theory. One of the cornerstone results so far was the decomposition of an commutative, finitely generated group (see here). This led to a split into elements of finite order and elements of infinite order where we have seen that the inherited Betti number is uniquely determined (see here). The remaining question yet to be answered concerns the uniqueness of the decomposition of the torsion part. In order to answer this question, the previous two stories about Sylow decomposition will have provided all the necessary tools (see here and here).
Group theory on its own appears very abstract and does not really reveal the promised applicability. But there is — and one of this I am going to describe in a more dedicated series.
Thank you for reading!
