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On Decomposing an Abelian p-Group Under a p′-Operator Group

On Decomposing an Abelian p-Group Under a p′-Operator Group Let A be a p′-group acting on a finite Abelian p-group P. We give a necessary and sufficient condition on an A-irreducible decomposition of Ω1(P) = ⊕ iɛ1 U i for the existence of an A-indecomposable decomposition of P = ⊕ iɛ1 R i such that Ω1(R i ) = U i for all i ɛ I. This readily implies a main result of [1]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

On Decomposing an Abelian p-Group Under a p′-Operator Group

Algebra Colloquium , Volume 7 (3) – Jan 1, 2000

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0291-y
Publisher site
See Article on Publisher Site

Abstract

Let A be a p′-group acting on a finite Abelian p-group P. We give a necessary and sufficient condition on an A-irreducible decomposition of Ω1(P) = ⊕ iɛ1 U i for the existence of an A-indecomposable decomposition of P = ⊕ iɛ1 R i such that Ω1(R i ) = U i for all i ɛ I. This readily implies a main result of [1].

Journal

Algebra ColloquiumSpringer Journals

Published: Jan 1, 2000

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