Vol. 22, No. 2, 1967

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Abelian p-groups determined by their Ulm sequences

Peter Crawley

Vol. 22 (1967), No. 2, 235–239

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.

Mathematical Subject Classification
Primary: 20.30
Received: 29 September 1966
Published: 1 August 1967
Peter Crawley