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Groups of Matrices With Integer Eigenvalues

Published online by Cambridge University Press:  09 April 2009

M. R. Freislich
M. R. Freislich
Affiliation:
University of New South Wales
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Let F be an algebraic number field, and S a subgroup of the general linear group GL(n, F). We shall call S a U-group if S satisfies the condition (U): Every x ∈ S is a matrix all of whose eigenvalues are algebraic integers. (This is equivalent to either of the following conditions: a) the eigenvalues of each matrix (x are all units as algebraic numbers; b) the characteristic polynomial for x has all its coefficients integers in F. In particular, then, every group of matrices with entries in the integers of F is a U-group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 3 , August 1971 , pp. 351 - 357
Copyright
Copyright © Australian Mathematical Society 1971

References

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