ω-elongations and Crawley’s problem

Alan Harvey Mekler and Saharon Shelah

Vol. 121 (1986), No. 1, 121–132

DOI: 10.2140/pjm.1986.121.121

Abstract

ω-elongations of Z(p) by separable p-primary groups are studied. Assuming (V = L), direct sums of cyclic groups are characterized using ω-elongations. Also assuming (V = L) much information is obtained about ω-elongations of Z(p) by groups which are not direct sums of cyclic groups. Finally it is shown that it is consistent that there is an uncountable group B with a countable basic subgroup such that there is a unique ω-elongation of Z(p) of B.

Mathematical Subject Classification 2000

Primary: 20K10

Secondary: 03E35, 03E45, 20A15, 20K40

Milestones

Received: 14 February 1984

Revised: 2 April 1985

Published: 1 January 1986