Vol. 32, No. 1, 1970

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Groups with maximum conditions

Bernhard Amberg

Vol. 32 (1970), No. 1, 9–19

It still seems to be unknown whether there exist Noetherian groups ( = groups with maximum condition on subgroups) that are not almost polycyclic, i.e., possess a soluble normal subgroup of finite index. However, the existence of even finitely generated infinite simple groups shows that in general a group whose subnormal subgroups satisfy the maximum condition need not be almost polycyclic. The following theorem gives a number of criteria for a group satisfying a weak form of the maximum condition to be almost polycyclic.

Mathematical Subject Classification
Primary: 20.54
Received: 15 May 1969
Published: 1 January 1970
Bernhard Amberg