Finite Groups of Order LEQ 6; Bijections and Group Operations

I’ve been talking about finite groups of small order in my class lately. In particular, examples of abelian and nonabelian groups and the notion of isomorphism classes of groups with a given order. I’ve written up some notes on the proof that all groups of order $\leq 5$ are abelian, and some notes on the isomorphism classes of groups of order $6$. Also, I wrote up some notes on using a bijection of sets $f: X \rightarrow G$, where $(G,\cdot)$ is a group, to define a unique group operation $\ast$ on $X$ such that $f: (X,\ast) \rightarrow (G,\cdot)$ is an isomorphism.

Advertisements
This entry was posted in math.GR and tagged , , . Bookmark the permalink.