section of a group

A section of a group $G$ isa quotient (http://planetmath.org/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 involved in a group $K$if $G$ is isomorphic to a section of $K$.

The relation ‘is involved in’ is transitive (http://planetmath.org/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 $K$.