Modular representations of metabelian groups
Author:
B. G. Basmaji
Journal:
Trans. Amer. Math. Soc. 169 (1972), 389-399
MSC:
Primary 20C20
DOI:
https://doi.org/10.1090/S0002-9947-1972-0310050-9
Addendum:
Trans. Amer. Math. Soc. 180 (1973), 507-508.
MathSciNet review:
0310050
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The irreducible modular representations, the blocks, and the defect groups of finite metabelian groups are determined. Also the dimensions of the principal indecomposable modules are computed.
- B. G. Basmaji, Monomial representations and metabelian groups, Nagoya Math. J. 35 (1969), 99–107. MR 244394
- Richard Brauer, Zur Darstellungstheorie der Gruppen endlicher Ordnung. II, Math. Z. 72 (1959/60), 25–46 (German). MR 108542, DOI https://doi.org/10.1007/BF01162934
- Richard Brauer, On blocks and sections in finite groups. I, Amer. J. Math. 89 (1967), 1115–1136. MR 219637, DOI https://doi.org/10.2307/2373422
- Richard Brauer, Some applications of the theory of blocks of characters of finite groups. IV, J. Algebra 17 (1971), 489–521. MR 281806, DOI https://doi.org/10.1016/0021-8693%2871%2990006-8
- A. H. Clifford, Representations induced in an invariant subgroup, Ann. of Math. (2) 38 (1937), no. 3, 533–550. MR 1503352, DOI https://doi.org/10.2307/1968599
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. MR 0144979
Retrieve articles in Transactions of the American Mathematical Society with MSC: 20C20
Retrieve articles in all journals with MSC: 20C20
Additional Information
Keywords:
Modular representations,
blocks,
defect groups,
principal indecomposable modules,
Brauer characters,
decomposition matrices,
Cartan matrices
Article copyright:
© Copyright 1972
American Mathematical Society
