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Theorems on multiple transitivity

Title: Theorems on multiple transitivity.
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Name(s): Zerla, Fredric J., author
Heerema, Nickolas, professor directing thesis.
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 1960
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (iii, 27 leaves)
Language(s): English
Abstract/Description: "The object of this paper is to present a number of theorems concerned with multiple transitivity in groups of permutations, culminating in a theorem of G. A. Miller on limits of transitivity of a group G in terms of the degree of G which is the number of letters on which the permutations of G act. The symmetric group consisting of all possible permutations on the n letters, is n - ply transitive. The alternating group, consisting of those permuations of the symmetric group which, when applied to the variables x₁,...,x[subscript n] carry the function [delta] = [pi] over i [lesser than] k (x[subscript i] - x[subscript k]) into itself, is (n-2) - ply transitive. In addition to the symmetric and alternating groups there are infinitely many groups which are 3 - ply transitive, but only a few groups known to be 4 - ply transitive. Using Miller's theorem it can be shown that for n [greater than] 12, a group of degree n cannot be t - fold transitive for t [less than or equal to] 3[square root of n]-2 unless the group is the symmetric or alternating group. Still better limits have been obtained since Miller published his theorem in 1915. Most recently, E. Parker obtained a limit with t of the order of magnitude 3[square root of n] for reasonable values of n”--Introduction.
Identifier: FSU_historic_AKP2819 (IID)
Bibliography Note: Includes bibliographical references (leaf 27).
Note(s): "January, 1960."
Typescript.
"Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Master of Science."
Advisor: Nickolas Heerema, Professor Directing Paper.
Subject(s): Permutations
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_historic_AKP2819
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Host Institution: FSU

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Zerla, F. J. (1960). Theorems on multiple transitivity. Retrieved from http://purl.flvc.org/fsu/fd/FSU_historic_AKP2819