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dc.contributor.authorCutler, Alanen_US
dc.date.accessioned2019-08-01T16:55:14Z
dc.date.issued1966
dc.date.submitted1966
dc.identifier.otherb14571195
dc.identifier.urihttps://hdl.handle.net/2144/36799
dc.descriptionThesis (M.A.)--Boston Universityen_US
dc.descriptionPLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.en_US
dc.description.abstractIn this paper we have determined the structure of divisible groups, certain primary groups, and countable torsion groups. Chapter 1 introduces two important infinite abelian groups, R and Z(p^∞). The structure of these groups is completely known and we have given most of the important properties of these groups in Chapter 1. Of special importance is the fact that a divisible group can be decomposed into a direct sum of groups each isomorphic to R or Z(p^∞). This is Theorem 2.12 and it classifies all divisible groups in terms of these two well-known groups. Theorem 1.6 is of great importance since it reduces the study of torsion groups to that of primary groups. We now have that Theorems 3.3 and 5.5 apply to countable torsion groups as well as primary groups. Theorem 3.3 gives a necessary and sufficient condition for an infinite torsion group to be a direct sum of cyclic groups. These conditions are more complicated than the finite case. From Theorem 3.3, we derived Corollary 3.5. This result is used later on to get that the Ulm factors of a group are direct sums of cyclic groups. In essence, Ulm's theorem says that a countable reduced primary group can be determined by knowing its Ulm type and its Ulm sequence. Now by Corollary 3.5, we have only to look at the number of cyclic direct summands of order p^n (for all integers n) for each Ulm factor. This gives us a system of invariants which we can assign to the group. Once again, these invariants are much harder to arrive at than in the finite case.en_US
dc.language.isoen_US
dc.publisherBoston Universityen_US
dc.subjectMathematicsen_US
dc.subjectInfinite abelian groupsen_US
dc.titleStructure theorems for infinite abelian groupsen_US
dc.typeThesis/Dissertationen_US
dc.description.embargo2031-01-01
etd.degree.nameMaster of Artsen_US
etd.degree.levelmastersen_US
etd.degree.disciplineMathematicsen_US
etd.degree.grantorBoston Universityen_US
dc.identifier.barcode11719025609597
dc.identifier.mmsid99181575650001161


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