Current Search: Kaufman, J. (x)
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Title
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Galois groups of prime degree and the O'Nan-Scott theorem.
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Creator
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Kaufman, J., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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Discussion begins with a modular method for determining cycle types of permutations in the Galois group of a given separable irreducible polynomial over Q. As the Galois group is a transitive permutation group on the n roots of its irreducible polynomial, a list of all transitive groups of degree n, together with the cycle type distributions of each group, allows a probablistic determination of the group in a process of elimination. In the case of prime degree, transitive groups are primitive...
Show moreDiscussion begins with a modular method for determining cycle types of permutations in the Galois group of a given separable irreducible polynomial over Q. As the Galois group is a transitive permutation group on the n roots of its irreducible polynomial, a list of all transitive groups of degree n, together with the cycle type distributions of each group, allows a probablistic determination of the group in a process of elimination. In the case of prime degree, transitive groups are primitive and by the O'Nan-Scott theorem are of restricted form. Theory is presented in order to arrive at these results and others, so that in conjunction with the classification theorem on finite simple groups, it is possible (in principle) to list all primitive permutation groups of particular prime degree. The case of degree 17 is examined to obtain a list of the transitive permutation groups of degree seventeen, as well as the cycle type of distributions of the groups identified.
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Date Issued
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1996
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PURL
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http://purl.flvc.org/fcla/dt/15289
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Subject Headings
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Mathematics
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Format
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Document (PDF)
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Title
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Investigations of a time dependent measurement technique for social judgment.
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Creator
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Kaufman, J., Florida Atlantic University, Vallacher, Robin R., Charles E. Schmidt College of Science, Department of Psychology
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Abstract/Description
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Argument is made for the use of variation permissive methods in the study of social judgment; one such dynamic method which purports to track on-line social evaluation (the mouse paradigm) is then introduced. The methodology of the mouse paradigm, which involves updating 'moment-to-moment' feelings via manipulation of a cursor by computer mouse, permits a wide range of experimental contrivance. Three varieties (SCALE, 1D and 2D), which differ in the amount of virtual (on screen) freedom of...
Show moreArgument is made for the use of variation permissive methods in the study of social judgment; one such dynamic method which purports to track on-line social evaluation (the mouse paradigm) is then introduced. The methodology of the mouse paradigm, which involves updating 'moment-to-moment' feelings via manipulation of a cursor by computer mouse, permits a wide range of experimental contrivance. Three varieties (SCALE, 1D and 2D), which differ in the amount of virtual (on screen) freedom of movement and psychological constraint, were tested with stereotyped targets (negative, ambivalent and positive) to determine any differences in their absolute distance time series and the extent to which aspects of these time series remained correlated with traditional scale-ratings of positivity and stability in feelings about targets. Results indicated a sharp difference between the two-dimensional (2D) variety and the one-dimensional varieties (SCALE and 1D), a finding which supports contention that the 2D variety possesses an appropriate balance of freedom and constraint.
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Date Issued
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1994
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PURL
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http://purl.flvc.org/fcla/dt/15003
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Subject Headings
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Judgment, Attitude change, Verbal behavior, Psychometrics, Permutation groups, Group theory, Galois theory
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Format
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Document (PDF)
