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ESSENTIALLY FINITELY INDECOMPOSABLE ABELIAN p-GROUPS

 

作者: Doyle Cutler,   John Irwin,  

 

期刊: Quaestiones Mathematicae  (Taylor Available online 1986)
卷期: Volume 9, issue 1-4  

页码: 135-148

 

ISSN:1607-3606

 

年代: 1986

 

DOI:10.1080/16073606.1986.9632111

 

出版商: Taylor & Francis Group

 

关键词: 20810;20K25;Primary abelian group;essentially finitely indecomposable;basic subgroup;final rank

 

数据来源: Taylor

 

摘要:

An abelian p-group C is said to be essentially finitely indecomposable (efi) if given any decomposition of G as the direct sum of a family of subgroups, there exists a positive integer n such that all but at moat a finite number of subgroups of this family are bounded by n. We look at examples and related questions. We prove that a reduced abelian p-group G is efi if and only if G modulo its elements of infinite height is efi. In the proof of this we obtain the following result which is of independent interest: Let A be a reduced p-group with a summand K such that K is a direct sum of cyclic groups. Let B be a basic subgroup of A. Then B contains a subgroup C such that C is a summand of A and the final rank of C is equal to the final rank of K.

 

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