diff --git a/chapter-3-cyclic-groups.tex b/chapter-3-cyclic-groups.tex index 044f1e0..843143f 100644 --- a/chapter-3-cyclic-groups.tex +++ b/chapter-3-cyclic-groups.tex @@ -1,6 +1,8 @@ \documentclass[./main.tex]{subfiles} \begin{document} + +\section{Cyclic groups} Groups are very general things, and thus we don't have much control over them. However, there are some groups which are much easier to understand and gain control over. These are the cyclic groups. Cyclic groups are very nice because @@ -231,7 +233,7 @@ isomorphic to any other cyclic group of order $n$. This means that any question about finite cyclic groups can be answered by studying $\bZ_n$ instead. -\subsection{Problems} +\subsection{Exercises and Problems} \begin{exercise}[Criterion for element to be identity] Prove that if $a^k = e$, then $k$ divides $\abs{a}$.