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Corrigenda On a classification of the function fields of algebraic tori: (Nagoya Math. J. 56 (1975), 85–104)

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo  and
Takehiko Miyata
Shizuo Endo
Affiliation:
Tokyo Metropolitan University, Osaka City University
Takehiko Miyata
Affiliation:
Tokyo Metropolitan University, Osaka City University
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There are some errors in Theorems 3.3 and 4.2 in [2]. In this note we would like to correct them.

1) In Theorem 3.3 (and [IV]), the condition (1) must be replaced by the following one;

(1) П is (i) a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of a cyclic group of order qf, q an odd prime, f ≧ 1, and a dihedral group of order 2m, m odd, where each prime divisor of m is a primitive qf-1(q — 1)-th root of unity modulo qf, or (iv) a generalized quaternion group of order 4m, m odd, where each prime divisor of m is congruent to 3 modulo 4.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 79 , October 1980 , pp. 187 - 190
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[ 1 ] Dress, A. W. M., The permutation class group of a finite group, J. of Pure and Applied Algebra, 6 (1975), 1–12.Google Scholar
[ 2 ] Endo, S. and Miyata, T., On a classification of the function fields of algebraic tori, Nagoya Math. J., 56 (1975), 85–104.Google Scholar