If in addition, each is a normal subgroup of , then the series is called a normal series.
A normal series in which is a maximal normal subgroup of contained in is called a principal series or a chief series.
Note that a composition series need not end in the trivial group . One speaks of a composition series (1) as a composition series from to . But the term composition series for generally means a composition series from to .
Similar remarks apply to principal series.
Some authors use normal series as a synonym for subnormal series. This usage is, of course, not compatible with the stronger definition of normal series given above.
|Date of creation||2013-03-22 13:58:42|
|Last modified on||2013-03-22 13:58:42|
|Last modified by||mclase (549)|