×
Cooperman, Gene; Hiss, Gerhard; Lux, Klaus; Müller, Jürgen

The Brauer tree of the principal \(19\)-block of the sporadic simple Thompson group. (English) Zbl 1115.20307

Exp. Math. 6, No. 4, 293-300 (1997).
Summary: This paper completes the construction of the Brauer tree of the sporadic simple Thompson group in characteristic \(19\). Our main computational tool to arrive at this result is a new parallel implementation of the DirectCondense method.

Cited in 5 Documents

MSC:

20C34 Representations of sporadic groups
20C40 Computational methods (representations of groups) (MSC2010)
20C20 Modular representations and characters

Keywords:

sporadic simple Thompson group; Brauer trees; principal block; modular characters; computation; condensation methods; modular representations; group algebras

Software:

ATLAS Group Representations; GAP; STAR/MPI; MeatAxe
Cite Review PDF
Full Text: DOI Euclid EuDML

References:

[1] Aho A. V., The design and analysis of computer algorithms (1975)
[2] Arlazarov V. L., DoH. Akad. Nauk SSSR 194 pp 487– (1970)
[3] Conway J. H., Atlas of finite groups (1985)
[4] Cooperman, G. ”STAR/MPI: Binding a parallel library to interactive symbolic algebra systems”. ISSAC 95: Proceedings of the International Symposium on Symbolic and Algebraic Computation. 1995, Montreal. Edited by: Levelt, A. H. M. pp.126–132. New York: ACM Press. [Cooperman 1995] · Zbl 0922.68079
[5] Cooperman, G. and Tselman, M. ”New sequential and parallel algorithms for generating high dimension Hecke algebras using the condensation technique”. ISSAC 96: Proceedings of the International Symposium on Symbolic and Algebraic Computation. Edited by: Lakshman, Y. N. pp.155–160. New York: ACM Press. [Cooperman and Tselman 1996], (Zurich, 1996) · Zbl 0916.20007
[6] Hiss G., Brauer trees of sporadic groups (1989) · Zbl 0685.20013
[7] Lux K., J. Symbolic Comput. 17 (6) pp 529– (1994) · Zbl 0828.16001 · doi:10.1006/jsco.1994.1033
[8] Pahlings H., Darstellungstheorietage pp 137– (1990)
[9] Parker R. A., Computational group theory pp 267– (1984)
[10] Ringe M., ”The C-MeatAxe” (1994)
[11] Ryba A. J. E., J. Symbolic Comput. 9 (5) pp 591– (1990) · Zbl 0705.20011 · doi:10.1016/S0747-7171(08)80076-4
[12] Schönert M., GAP: Groups, algorithms, and programming (1994)
[13] Thackray J. G., Ph.D. thesis, in: Modular representations of finite groups (1981)
[14] Wilson R. A., ”Atlas of finite group representations” (1996)
[15] Wilson R. A., J. Algebra 184 (2) pp 505– (1996) · Zbl 0855.20034 · doi:10.1006/jabr.1996.0271
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.