  Classes SSGP(n)(n < \omega) of topological groups are defined, and the
class-theoretic inclusions SSGP(n) \subseteq SSGP(n+1) \subseteq m.a.p. are
established and shown proper. These classes are investigated with respect to
the properties normally studied by topologists (products, quotients, passage to
dense subgroups, and the like).
  In passing the authors establish the presence of the SSGP(1) or SSGP(2)
property in many of the early examples in the literature of abelian m.a.p.
groups.
