Accession Number:

AD0627630

Title:

UNIMODULAR GROUP MATRICES WITH RATIONAL INTEGERS AS ELEMENTS,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV SANTA BARBARA DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1963-08-20

Pagination or Media Count:

9.0

Abstract:

The following theorem is proved For a finite solvable group G, A is a unimodular matrix of rational integers such that B AA is a group matrix for G. Then A A sub 1 T where A sub 1 is a unimodular group matrix of rational integers for G and T is a generalized permutation matrix. The left regular representation of G is defined by the matrix equations gg sub 1, gg sub 2, gg sub n g sub 1, g sub 2, ..., g sub n PL g where g sub 1, g sub 2, ..., g sub n are ordered elements of G and g E G. The right regular representation is similarly defined. Their group rings, the set of all linear combinations of PL g and PR g, are denoted LG and RG. It is noted that matrices in LG and RG commute, and a matrix that commutes with any PR g is a member of LG. These facts are used in an inductive proof on an ordered, ascending chain of subgroups of G to obtain the theorem. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE