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. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/37036 |
| Date | January 1966 |
| Creators | Mitton, David |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| 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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