On the field of a $2$-block
HTML articles powered by AMS MathViewer
- by B. G. Basmaji PDF
- Proc. Amer. Math. Soc. 83 (1981), 471-475 Request permission
Abstract:
For a $p$-block $B$ satisfying some conditions, a field $Q(B)$ is defined. It is proved that for a $2$-block $B$ of a finite metabelian group $G$, $Q(B) = Q(\theta )$ for some irreducible character $\theta$ in $B$ if the $2$-Sylow subgroup $P$ of the commutator group $Gā$ is cyclic. This is shown to be false in general.References
- B. G. Basmaji, Monomial representations and metabelian groups, Nagoya Math. J. 35 (1969), 99ā107. MR 244394
- B. G. Basmaji, Modular representations of metabelian groups, Trans. Amer. Math. Soc. 169 (1972), 389ā399. MR 310050, DOI 10.1090/S0002-9947-1972-0310050-9
- Richard Brauer, Some applications of the theory of blocks of characters of finite groups. IV, J. Algebra 17 (1971), 489ā521. MR 281806, DOI 10.1016/0021-8693(71)90006-8
- 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, Inc.), New York-London, 1962. MR 0144979
- R. Gow, Real-valued and $2$-rational group characters, J. Algebra 61 (1979), no.Ā 2, 388ā413. MR 559848, DOI 10.1016/0021-8693(79)90288-6
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 471-475
- MSC: Primary 20C15; Secondary 20C20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627672-9
- MathSciNet review: 627672