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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