small in 4.5

group.tex

@@ -1844,9 +1844,9 @@ \section{The sign homomorphism}
 $\Aut(A)$ to $\SG_2$ for each $A$, since it does so for $A \jdeq
 \sh_{\SG_n}$. Even better, this abstract homomorphism comes from a concrete one
 $\sgn^A : \Hom(\Aut(A),\SG_2)$ for each finite set $A$. Indeed, since
-$T \eqto U$ is a 2-element set for any 2-element sets $T$ and $U$, we can
-consider the map $\Bsgn^A_\div : \BAut(A) \to \BSG_2$ that associates
-$B : \BAut(A)$ with $(\Bsgn_\div(A) \eqto \Bsgn_\div(B))$. The identification of
+$T \eqto U$ is a $2$-element set for any $2$-element sets $T$ and $U$, we can
+consider the map $\Bsgn^A_\div : \BAut(A) \to \BSG_2$ that maps
+$B : \BAut(A)$ to $(\Bsgn_\div(A) \eqto \Bsgn_\div(B))$. The identification of
 $\Bsgn^A_\div(A)$ with $\{\pm1\}$ mentioned above makes $\Bsgn^A_\div$ into a
 pointed map $\Bsgn^A : \BAut(A) \ptdto \BSG_2$, i.e., it defines an homomorphism
 $\sgn^A : \Hom(\Aut(A),\SG_2)$, as announced.%