WIP 4.4 and 4.5

fingp.tex

@@ -54,9 +54,7 @@ \section{Lagrange's theorem, counting version}
 We start our investigation by giving the version of Lagrange's theorem which has to do with counting, but first we pin down some language.
 \begin{definition}
   \label{def:finitegrd}
-A \emph{finite group}\index{finite group} is a group such that the set $\USym G$ is finite.   If $G$ is a finite group, then the \emph{\gporder}\index{\gporder} $|G|$ is the cardinality of the finite set $\USym G$ (\ie $\USym G:\fin_{|G|}$).
-% Let $n:\NN$ be positive.
-% A \emph{finite group of \gporder $n$}\index{finite group! of \gporder $n$} is a group $G$ such that the set $\USym G$ is in $\fin_n$.
+A \emph{finite group}\index{finite group} is a group such that the set $\USym G$ is finite.   If $G$ is a finite group, then the \emph{\gporder}\index{\gporder} $|G|$ is the cardinality of the finite set $\USymG$ (\ie $\USymG:\conncomp\FinSet{|G|}$).
 \end{definition}
 \begin{example}
   The trivial group has \gporder $1$, the cyclic group $C_n$ of order $n$ has \gporder $n$ %(which is good)