Subgroup Series Ii
نویسنده
چکیده
in which GiCG and Gi+1/Gi ⊂ Z(G/Gi) for all i. We call G solvable if it admits a normal series (1.1) in which Gi+1/Gi is abelian for all i. Every nilpotent group is solvable. Nilpotent groups include finite p-groups, and some theorems about p-groups extend to nilpotent groups (e.g., any nontrivial normal subgroup of a nilpotent group has a nontrivial intersection with the center). There is a large number of characterizations of nilpotency for finite groups.
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