Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T04:18:10.552Z Has data issue: false hasContentIssue false
  • English
  • Français

On Block Idempotents of Modular Group Rings

Published online by Cambridge University Press:  22 January 2016

Masaru Osima
Masaru Osima*
Affiliation:
Osaka University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a group G of finite order g = pag′ where p is a prime number and (p, g′) = 1. Let Ω be the algebraic number field which contains the p-th roots of unity. Let K1, K2,…, Kn be the classes of conjugate elements in G and the first m(≦n) classes be p-regular. There exist n distinct (absolutely) irreducible characters x1, x2,…, xn of G.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 429 - 433
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung, I, Math. Zeits. 63 (1956), 406–444.CrossRefGoogle Scholar
[2] Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung, II, Math. Zeits. 72 (1959), 25–46.Google Scholar
[3] Brauer, R., Some applications of the theory of blocks of characters of finite groups, I, J. Alg. 1 (1964), 152–167.Google Scholar
[4] Brauer, R. and Feit, W., On the number of irreducible characters of finite groups in a given block. Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 361–365.Google Scholar
[5] Curtis, C. W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras, Interscience, New York, London, 1962.Google Scholar
[6] Osima, M., Notes on blocks of group characters, Math. J. Okayama Univ. 4 (1955), 175–188.Google Scholar
[7] Osima, M., On a theorem of Brauer, Proc. Japan Acad. 40 (1964), 795–798.Google Scholar