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Cancellation in direct products of loops
Crown, Gary D.
Crown, Gary D.
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t1962_Crown.pdf
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1962-06
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Abstract
In the examination of the structure of certain classes
of Abelian groups, the question arises, “Given a class of
Abelian groups satisfying a certain structure theorem A,
then is theorem A really applicable, or is theorem A so
complicated and restricted that it is absolutely useless?"
Kaplansky [1] proposed a list of three test problems for
which he stated that, if theorem A can produce satisfactory
results to these three test problems, then this might be
a test of the usefulness of this class of Abelian groups.
However, Walker [l], proved that test problem III, of
Kaplansky, was true for all Abelian groups, and thus it
cannot serve as a test for the usefulness of a certain
theorem which applies only to a certain class of Abelian
groups. It is the purpose of this thesis to generalize
some of the main results of Walker's thesis, which lead
up to the solution of Kaplansky's test problem III, to
the more general case of a loop.
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Thesis (M.S.)-- University of Wichita, College of Liberal Arts and Sciences, Dept. of Mathematics
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Wichita State University
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Wichita State University