411 REFERENCE · Wikibooks
Group Theory/Subnormal subgroups and series
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{{definition|subnormal subgroup|Let be a group. A subgroup is called subnormal subgroup if and only if there exists
subnormal series Let be a group. Then a subnormal series is a finite family of subgroups such that
,
where is the identity.
composition series Let be a group. A composition series of is a subnormal series
of such that for all the quotient group is simple.
Schreier refinement theorem Let be a group, and let
be a subnormal series of .