On the units of the integral group ring of a dihedral group

Takehiko MIYATA

doi:10.2969/jmsj/03240703

Takehiko MIYATA

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 4 Pages 703-708

DOI https://doi.org/10.2969/jmsj/03240703

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Published: 1980 Received: November 20, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J.A. Cohn and D. Livingstone, On the structure of group algebras, I, Canad, J. Math., 17 (1965), 583-593.
2) R.K. Dennis, The structure of the unit group of rings, In: Ring Theory II, Marcel. Dekker, 1977.
3) S. Endo and T. Miyata, On the class groups of dihedral groups, (to appear).
4) I. Hughes and K.R. Pearson, The group of units of the integral group ring ZS₃, Canad. Math. Bull., 15 (1972), 529-534.
5) J.M. Masley, Solution of small class number problems for cyclotomic fields, Compositio Math., 33 (1976), 179-186.
6) T. Miyata, A normal integral basis theorem for dihedral groups, (to appear).
7) D.S. Passman, Isomorphic groups and group rings, Pacific J. Math., 15 (1965), 561-583.
8) I. Reiner and S. Ullom, A Mayer-Vietoris sequences for class groups, J. Algebra, 31 (1974), 305-342.
9) A. Fröhlich, I. Reiner and S. Ullom, Class groups and Picard groups of orders, Proc. London Math. Soc., (3) 29 (1974), 405-434.

Right : [1] J. A. Cohn and D. Livingstone, On the structure of group algebras, I, Canad, J. Math., 17 (1965), 583-593.
[2] R. K. Dennis, The structure of the unit group of rings, In: Ring Theory II, Marcel. Dekker, 1977.
[3] S. Endo and T. Miyata, On the class groups of dihedral groups, (to appear).
[4] I. Hughes and K.R. Pearson, The group of units of the integral group ring ZS₃, Canad. Math. Bull., 15 (1972), 529-534.
[5] J. M. Masley, Solution of small class number problems for cyclotomic fields, Compositio Math., 33 (1976), 179-186.
[6] T. Miyata, A normal integral basis theorem for dihedral groups, (to appear).
[7] D. S. Passman, Isomorphic groups and group rings, Pacific J. Math., 15 (1965), 561-583.
[8] I. Reiner and S. Ullom, A Mayer-Vietoris sequences for class groups, J. Algebra, 31 (1974), 305-342.
[9] A. Fröhlich, I. Reiner and S. Ullom, Class groups and Picard groups of orders, Proc. London Math. Soc., (3) 29 (1974), 405-434.

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