Ulm’s theorem asserts that,
within the class of all reduced countable abelian p-groups, a group is determined, up
to isomorphism, by its Ulm sequence. Although this theorem fails in general for
uncountable groups, there are classes of uncountable abelian p-groups whose
members are determined within the class by their Ulm sequences. Kolettis has shown
that the class of direct sums of countable p-groups has this property. Here it is shown
that the class of those abelian p-groups for which the Ulm type is finite and all the
Ulm factors except the last are direct sums of cyclic groups, is another such
class.
