Every finite group 
of order greater than one possesses a finite series of subgroups, called a composition series, such that
 |
where 
is a maximal subgroup of 
and 
means that 
is a normal subgroup of
.
A composition series is therefore a normal series
without repetition whose factors are all simple (Scott 1987, p. 36).
The quotient groups 
, 
, ..., 
, 
are called composition quotient groups.
