Renfrow, James Thomas (1969) A study of rank four permutation groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-09272002-154545
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In this thesis we study rank 4 permutation groups. A rank 4 group is a finite transitive permutation group acting on a set [Omega] such that the subgroup fixing a letter breaks up [Omega] into 4 orbits. The main tool employed in examining rank 4 groups is the use of intersection matrices, an idea introduced by Donald Higman. Intersection matrices are used to obtain relations between the lengths of the four orbits associated with a rank 4 representation and the degrees of the irreducible characters in the permutation character of the representation. It is shown that two orbits of the representation are paired if and only if two of the characters are complex conjugates of one another. All the maximal primitive rank 4 groups are determined.
Techniques are developed, using intersection matrices, to find all rank 4 representations of known finite groups. Group theoretic results about possible rank 4 groups are derived from the intersection matrices which would have to correspond to the rank 4 representation.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||2 April 1969|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||30 Sep 2002|
|Last Modified:||26 Dec 2012 03:03|
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