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The tensor product of two abelian groups Mitton, David
Abstract
The concept of a free group is discussed first in Chapter 1 and in Chapter 2 the tensor product of two groups for which we write A⊗B is defined by "factoring out" an appropriate subgroup of the free group on the Cartesian product of the two groups. The existence of a unique homomorphism h : A⊗B→H is assured by the existence of a bilinear map f : A×B→H , where H is any group (Lemma 2-2) and this property of the tensor product is used extensively throughout the thesis. In Chapter 3 the complete characterization is given for the tensor product of two arbitrary finitely generated groups. In the last chapter we discuss the structure of A⊗B for arbitrary groups. Essentially, the only complete characterizations are for those cases where one of the two groups is torsion. Many theorems from the theory of Abelian Groups are assumed but some considered interesting are proved herein.
Item Metadata
Title |
The tensor product of two abelian groups
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1966
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Description |
The concept of a free group is discussed first in Chapter 1 and in Chapter 2 the tensor product of two groups for which we write A⊗B is defined by "factoring out" an appropriate subgroup of the free group on the Cartesian product of the two groups. The existence of a unique homomorphism h : A⊗B→H is assured by the existence of a bilinear map f : A×B→H , where H is any group (Lemma 2-2) and this property of the tensor product is used extensively throughout the thesis. In Chapter 3 the complete characterization is given for the tensor product of two arbitrary finitely generated groups. In the last chapter we discuss the structure of A⊗B for arbitrary groups. Essentially, the only complete characterizations are for those cases where one of the two groups is torsion. Many theorems from the theory of Abelian Groups are assumed but some considered interesting are proved herein.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-08-31
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080558
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.