Vol. 23, No. 1, 1967

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Disjoint basic subgroups

Alfred Richard Mitchell and Roger W. Mitchell

Vol. 23 (1967), No. 1, 119–127

This paper arose from consideration of the following questions. First, what characterizes those infinite Abelian reduced p-groups which possess disjoint basic subgroups? Second, are there properties that a basic subgroup must possess to insure the existence of a basic subgroup disjoint from it? We show that a necessary and sufficient condition for an infinite Abelian reduced p-group G to contain disjoint basic subgroups is that |G|=final rank G. Futhermore, in such a group a necessary and sufficient condition for a basic subgroup B to have a basic subgroup disjoint from it is that B is a lower basic subgroup of G.

Mathematical Subject Classification
Primary: 20.30
Received: 14 July 1966
Published: 1 October 1967
Alfred Richard Mitchell
Roger W. Mitchell