Vol. 29, No. 1, 1969

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A quasi-decomposable abelian group without proper isomorphic quotient groups and proper isomorphic subgroups

John McCormick Irwin and Takashi Ito

Vol. 29 (1969), No. 1, 151–160

All of the group in this paper are abelian p-groups without elements of infinite height. A group is said to be quasiindecomposable if whenever H is a summand of G then either H or G∕H is finite. The p-socle of G is the sub-group consisting of all the elements x in G such that px = 0.

In this paper it is shown that there are conditions that can be imposed on the socle of G which are sufficient for G to (a) have no proper isomorphic subgroups; (b) have no proper isomorphic quotient groups; and (c) be quasiindecomposable. Furthermore, it is shown that groups which make these results meaningful actually exist.

Mathematical Subject Classification
Primary: 20.30
Received: 22 August 1967
Published: 1 April 1969
John McCormick Irwin
Takashi Ito