Noetherian group

group with the maximum condition for subgroups

A group in which every strictly ascending chain of subgroups is finite. This class is named after E. Noether, who investigated rings with the maximum condition for ideals — Noetherian rings (cf. Noetherian ring). Subgroups and quotient groups of a Noetherian group are Noetherian. Examples have been constructed of Noetherian groups that are not finite extensions of polycyclic groups (cf. Polycyclic group) [1].

References

[1]	A.Yu. Ol'shanskii, "Infinite groups with cyclic subgroups" Soviet Math. Dokl. , 20 : 2 (1979) pp. 343–346 Dokl. Akad. Nauk SSSR , 245 : 4 (1979) pp. 785–787