Abstract
Our aim in this note is to generalize results of Baer in [3;
5]. In § 1 an arbitrary formation n is considered,
the key result being Proposition 1.5. This is applied in § 2 to characterize
various finiteness conditions, for example the classes of groups with
maximum [minimum] condition on subgroups, subnormal subgroups, and normal
subgroups respectively, or the class of (not necessarily soluble)
polyminimax groups (see Theorems 2.1 and 2.6). These results may also be
regarded as generalizations of the well-known theorem of Malcev-Baer that a
radical group satisfies the maximum condition [is a polyminimax group] if
all its abelian subgroups satisfy the maximum condition [are minimax
groups].
Publisher
Canadian Mathematical Society