"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. / "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. / Includes bibliographical references (leaf 27).
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_257291 |
| Contributors | Zerla, Fredric J. (authoraut), Heerema, Nickolas (professor directing thesis.), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (iii, 27 leaves), computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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