subnormal series (original) (raw)

If in addition, each Gi is a normal subgroup of G, then the series is called a normal series.

A normal series in which Gi is a maximal normal subgroup of G contained in Gi-1is called a principal series or a chief series.

Note that a composition series need not end in the trivial group 1. One speaks of a composition series (1) as a composition series from G to H. But the term _composition series for G_generally means a composition series from G to 1.

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.