SectionOfAGroup 2007-06-13 13:58:30 2007-06-15 02:23:52 Definition involved in \PMlinkescapeword{means} \PMlinkescapeword{relation} \PMlinkescapeword{structure} A \emph{section} of a group $G$ is a \PMlinkname{quotient}{QuotientGroup} of a subgroup of $G$. That is, a section of $G$ is a group of the form $H/N$, where $H$ is a subgroup of $G$, and $N$ is a normal subgroup of $H$. A group $G$ is said to be \emph{involved in} a group $K$ if $G$ is isomorphic to a section of $K$. The relation `is involved in' is \PMlinkname{transitive}{Transitive3}, that is, if $G$ is involved in $K$ and $K$ is involved in $L$, then $G$ is involved in $L$. Intuitively, `$G$ is involved in $K$' means that all of the structure of $G$ can be found inside $K$.