Author Archives: Horace Fusco

I hope you enjoy reading about Property and expanding graphs! Thank you everyone for making Geometric Group theory a wonderful class!! (Edit: Sorry for the super late update, I meant to do this at the beginning of break but apparently … Continue reading →

We left off our discussion of regular languages with dashed hopes when we learned that is a regular language if and only if is finite. This means that dealing with , the set of words on the generators of which … Continue reading →

I’ll begin my second (!) blog post about free groups by recalling a proposition that cuts right to the heart of what a free group is. Universal property. Let be a generating set. Then is the unique froups os that … Continue reading →

Free groups are a wonderful source of examples, counterexamples, and play a crucial role in some pretty slick constructions. For instance, the famous Banach-Tarski paradox utilizes a construction which, at its heart, boils down to a fact about free groups, … Continue reading →