Characterization of the simple components of the group algebras over the p-adic number field

Toshihiko YAMADA

doi:10.2969/jmsj/02320295

Toshihiko YAMADA

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JOURNAL FREE ACCESS

1971 Volume 23 Issue 2 Pages 295-310

DOI https://doi.org/10.2969/jmsj/02320295

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Published: 1971 Received: April 27, 1970 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Brauer, On the representations of groups of finite order, Proc. Internat. Congress, Cambridge, 1950, vol. 2, 33-36.
2) R. Brauer, On the algebraic structure of group rings, J. Math. Soc. Japan, 3 (1951), 237-251.
3) R. Brauer, Representations of finite groups, Lectures on modern mathematics, edited by T. L. Saaty, vol. I, 133-175, John Wiley & Sons, New York, 1963.
4) C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
5) M. Deuring, Algebren, Springer, Berlin, 1935.
6) W. Feit, Characters of finite groups, Benjamin, New York, 1967.
7) B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967.
8) J.-P. Serre, Corps locaux, Hermann, Paris, 1962.
9) L. Solomon, The representation of finite groups in algebraic number fields, J. Math. Soc. Japan, 13 (1961), 144-164.
10) E. Weiss, Cohomology of groups, Academic Press, New York, 1969.
11) E. Witt, Die algebraische Struktur des Gruppenringes einer endlichen Gruppe über einem Zahlkörper, J. Reine Angew. Math., 190 (1952), 231-245.
12) T. Yamada, On the group algebras of metabelian groups over algebraic number fields II, J. Fac. Sci. Univ. Tokyo, 16 (1969), 83-90.
13) T. Yamada, On the Schur index of a monomial representation, Proc. Japan Acad., 45 (1969), 522-525.
14) H. Zassenhaus, The theory of groups, 2nd ed., Chelsea, New York, 1958.

Right : [1] R. Brauer, On the representations of groups of finite order, Proc. Internat. Congress, Cambridge, 1950, vol. 2, 33-36.
[2] R. Brauer, On the algebraic structure of group rings, J. Math. Soc. Japan, 3 (1951), 237-251.
[3] R. Brauer, Representations of finite groups, Lectures on modern mathematics, edited by T. L. Saaty, vol. I, 133-175, John Wiley & Sons, New York, 1963.
[4] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
[5] M. Deuring, Algebren, Springer, Berlin, 1935.
[6] W. Feit, Characters of finite groups, Benjamin, New York, 1967.
[7] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967.
[8] J. -P. Serre, Corps locaux, Hermann, Paris, 1962.
[9] L. Solomon, The representation of finite groups in algebraic number fields, J. Math. Soc. Japan, 13 (1961), 144-164.
[10] E. Weiss, Cohomology of groups, Academic Press, New York, 1969.
[11] E. Witt, Die algebraische Struktur des Gruppenringes einer endlichen Gruppe über einem Zahlkörper, J. Reine Angew. Math., 190 (1952), 231-245.
[12] T. Yamada, On the group algebras of metabelian groups over algebraic number fields II, J. Fac. Sci. Univ. Tokyo, 16 (1969), 83-90.
[13] T. Yamada, On the Schur index of a monomial representation, Proc. Japan Acad., 45 (1969), 522-525.
[14] H. Zassenhaus, The theory of groups, 2nd ed., Chelsea, New York, 1958.

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