NICE ELONGATIONS OF PRIMARY ABELIAN GROUPS

作者：Danchev Peter V^*; Keef Patrick W

来源：Publicacions Matematiques, 2010, 54(2): 317-339.

• Nice subgroups
• elongations
• abelian groups
• omega(1)-homomorphisms

Suppose N is a nice subgroup of the primary abelian group C; and A = G/N. The paper discusses various contexts in which satisfying some property implies that A also satisfies the property; or visa versa, especially when N is countable. For example, if n is a positive integer, C has length not exceeding omega(1) and N is countable, then G is n-summable if A is n-summable. When A is separable and N is countable, we discuss the condition that any such G decomposes into the direct sum of a countable and a separable group, and we show that it is undecidable in ZFC whether this condition implies that A must be a direct sum of cyclics. We also relate these considerations to the study of nice bases for primary abelian groups.

• 出版日期2010