On mixed groups of torsion-free rank one with totally projective primary components

Wallace, Kyle D.

doi:10.1016/0021-8693(71)90005-6

Cited by 41 publications

(17 citation statements)

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“…Since {x,} is part of a decomposition basis, each height matrix is the minimum of the height matrices of the {xj terms. In going from (8) to (7), the terms H(m k b n x n ), H(m k d n x n+[ ) and H(m k a n c n X-n ) are added to the right hand side of (8). The terms…”

Section: Robert O Stantonmentioning

confidence: 99%

“…For q -indicators, it suffices to show that m k b n x n may be added to the right hand side of (8) and that (10a), (10b), and (10c) may be deleted from the left hand side. For an integer rc, n' now denotes the q -factor of n.…”

Section: Robert O Stantonmentioning

confidence: 99%

“…with the latter term in the left hand side of (8), and so (10a Furthermore, from the first terms of (16) and (17), we have no difficulties unless…”

mentioning

confidence: 97%

“…This definition is due to Wallace [8]. His techniques yield the following version of the generalization of Ulm's theorem (see Hill [3], Walker [7]).…”

mentioning

confidence: 99%

“…In Case B, (k is odd, k ^ 3), we add m k a n c n x-n~\ and m k d n x n+λ to both sides of (8). These terms cause no problems.…”

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confidence: 99%

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Infinite decomposition bases

Stanton¹

1977

Pacific J. Math.

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The concept of decomposition basis is essential to the study of the structure of mixed abelian groups. The main theorem of this paper uses invariants previously defined by the author to determine the decomposition bases of a given group. This is used to extend Ulm's theorem for mixed abelian groups to the entire class of affable groups.1. Introduction. The word "group" will mean abelian group throughout. If X is a subset of a group A, [X] denotes the subgroup generated by X. A, (A p ) represents the torsion part (p-component) of the group A, where p is a prime. Z will denote the integers, while Q represents the rationals. Standard terminology (refer to Fuchs

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Section: Robert O Stantonmentioning

confidence: 99%

Section: Robert O Stantonmentioning

confidence: 99%

“…with the latter term in the left hand side of (8), and so (10a Furthermore, from the first terms of (16) and (17), we have no difficulties unless…”

mentioning

confidence: 97%

“…This definition is due to Wallace [8]. His techniques yield the following version of the generalization of Ulm's theorem (see Hill [3], Walker [7]).…”

mentioning

confidence: 99%

“…In Case B, (k is odd, k ^ 3), we add m k a n c n x-n~\ and m k d n x n+λ to both sides of (8). These terms cause no problems.…”

mentioning

confidence: 99%

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