Let
denote the class of all (fully) ordered groups satisfying the maximal condition on subgroups, and let
denote the class of all locally
groups. In this paper we investigate the family of convex subgroups of
groups.
It is well known (see [1, pp. 51, 54]) that every convex subgroup of an
is normal in G, and for any jump D –< C in the family of convex subgroups, [G′, C] ⊆ D. We observe that these properties are also true for any
group and record, without proof, the following.
THEOREM 1. Any convex subgroup of an
group G is normal in G, and for any jump D –< C in the family of convex subgroups, [G′, C] ⊆ D.