Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-22T10:57:06.619Z Has data issue: false hasContentIssue false
  • English
  • Français

Central idempotents in p-adic group rings

Part of: Rings and algebras arising under various constructions Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Burkhard Külshammer
Burkhard Külshammer
Affiliation:
Universität Augsburg, Augsburg, Germany
Rights & Permissions [Opens in a new window]

Abstract

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 provide character-free proofs of some results on idempotents in p-adic group rings, centering around Brauer's Second Main Theorem on Blocks.

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 20C11: $p$-adic representations of finite groups 20C20: Modular representations and characters 16S34: Group rings , Laurent polynomial rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 2 , April 1994 , pp. 278 - 289
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Brauer, R., ‘Zur Darstellungstheorie der Gruppen endlicher Ordnung II’, Math. Z. 72 (1959), 25–46.Google Scholar
[2]Broué, M., ‘Radical, hauteurs, p-sections et blocs’, Ann. Math. 107 (1978), 89–107.Google Scholar
[3]Cliff, G., ‘Zero divisors and idempotents in group rings’, Canad. J. Math. 32 (1980), 596–602.Google Scholar
[4]Cohen, M. and Montgomery, S., ‘Group-graded rings, smash products, and group actions’, Trans. Amer. Math. Soc. 282 (1984), 237–258.CrossRefGoogle Scholar
[5]Curtis, C. and Reiner, I., Methods of representation theory Vol. II (J. Wiley, New York, 1987).Google Scholar
[6]Dade, E.C., ‘On Brauer's second main theorem’, J. Algebra 2 (1965), 299–311.Google Scholar
[7]Dornhoff, L., Group representation theory Part B (Marcel Dekker, New York, 1972).Google Scholar
[8]Feit, W., The representation theory of finite groups (North-Holland, Amsterdam, 1982).Google Scholar
[9]Goldschmidt, D., Lectures on character theory (Publish or Perish, Berkeley, 1980).Google Scholar
[10]Huppert, B. and Blackburn, N., Finite Groups II (Springer, Berlin, 1982).CrossRefGoogle Scholar
[11]Iizuka, K., ‘On Brauer's theorem on sections in the theory of group characters’, Math. Z. 75 (1961), 299–304.Google Scholar
[12]Külshammer, B., ‘Group-theoretical descriptions of ring-theoretical invariants of group algebras’, in: Representation theory of finite groups and finite-dimensional algebras (Birkhäuser, Basel, 1991).Google Scholar
[13]Külshammer, B., Lectures on block theory (Cambridge Univ. Press, London, 1991).Google Scholar
[14]Landrock, P., Finite group algebras and their modules (Cambridge Univ. Press, London, 1983).Google Scholar
[15]Nagao, H., ‘A proof of Brauer's theorem on generalized decomposition numbers’, Nagoya J. Math. 22 (1963), 73–77.Google Scholar
[16]Nagao, H. and Tsushima, Y., Representations of finite groups (Academic Press, Boston, 1989).Google Scholar
[17]Oliver, R., Whitehead groups of finite groups (Cambridge Univ. Press, London, 1988).Google Scholar
[18]Puig, L., ‘Sur un théorème de Green’, Math. Z. 166 (1979), 117–129.Google Scholar
[19]Puig, L., ‘Pointed groups and construction of characters’, Math. Z. 176 (1981), 265–292.Google Scholar
[20]Taylor, M., Class groups of group rings (Cambridge Univ. Press, London, 1984).Google Scholar