Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, 1922. / Vita. "Private edition, distributed by the University of Chicago Libraries, Chicago, Illinois." "Reprinted from American journal of mathematics, vol. XLIV, no. 4, October, 1922." Includes bibliographical references.

Thesis (Ph. D.)--Cornell University. / From the American journal of mathematics, v. 26, no. 1.

Thesis (Ph. D.)--Cornell University. / From the American journal of mathematics, v. 26, no. 1.

No description available.

The units in the group ring for S₃ over the integers are investigated. It is shown that the only units of finite order are of order two, three or six. Infinite classes of units of each of these orders are constructed as well as an infinite class of units of infinite order. The equation G = AA T, where G is a unimodular group matrix of rational integers and A a matrix of rational integers, is investigated in the ring of group matrices for S₃. It is shown that A = CP, where C is a unimodular group matrix of rational integers and P a generalized permutation matrix. It is also shown that if H is a positive definite symmetric unimodular group matrix then H = H₁H₁ T where H₁ is a group matrix of rational integers and H is of infinite order except in the trivial case when H = I. / Science, Faculty of / Mathematics, Department of / Graduate

One of the existing methods of calculating the characters of irreducible representations of space groups and double space groups is described in some detail, and applied to the case of the non-symmorphic space group D¹⁹ ₄h (I4₁/amd) (which is the space group of crystals of white tin). A complete list of the characters of irreducible representations of this space group and the corresponding double group is given. Some useful relations involving the characters are also included. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this thesis we obtain all the ordinary irreducible characters of Weyl groups of rank ≤4 by using MacDonald' s method. This method enables us to find almost all the characters, and the remaining ones may be obtained by combining MacDonald characters and characters of exterior products of the reflection representation. / Science, Faculty of / Mathematics, Department of / Graduate

Let G he the direct sum of n ≥ 2 copies of the cyclic group, Z , of integers. Let p be a fixed prime and α ≥ 1 a fixed integer. Consider the subgroups, λ , of G of index p[superscript]α in G . Let S be a subset of G. We say S is a stellar set if ax ε S implies (1.1) x,2x,...,ax ε S for any x ε G and any integer a ≥ 1 . Suppose S is a stellar set, p[superscript]α G ∩ S = ∅, and S intersects all the subgroups λ of G of index p[superscript]α in G . We shall show that then |S| ≥ p[superscript]α + P[superscript]α-1. / Science, Faculty of / Mathematics, Department of / Graduate