Morten E. Harris
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) = ⊕iɛ1U i for the existence of an A-indecomposable decomposition of P = ⊕iɛ1R i such that Ω1(R i ) = U i for all i ɛ I. This readily implies a main result of [1].
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
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) = ⊕iɛ1U i for the existence of an A-indecomposable decomposition of P = ⊕iɛ1R i such that Ω1(R i ) = U i for all i ɛ I. This readily implies a main result of [1].
Key concepts: Mathematics, Indecomposable module, Abelian group, Group (periodic table), Decomposition, Combinatorics, Pure mathematics, Operator (biology)