Groups with faithful blocks
HTML articles powered by AMS MathViewer
- by H. Pahlings PDF
- Proc. Amer. Math. Soc. 51 (1975), 37-40 Request permission
Abstract:
A necessary and sufficient condition is given for a finite group to have a $p$-block with kernel 1. This extends a theorem of Gaschütz on the existence of a faithful irreducible representation of a finite group.References
- Richard Brauer, Some applications of the theory of blocks of characters of finite groups. I, J. Algebra 1 (1964), 152–167. MR 168662, DOI 10.1016/0021-8693(64)90031-6
- Wolfgang Gaschütz, Endliche Gruppen mit treuen absolut-irreduziblen Darstellungen, Math. Nachr. 12 (1954), 253–255 (German). MR 67115, DOI 10.1002/mana.19540120308
- Gerhard O. Michler, The kernel of a block of a group algebra, Proc. Amer. Math. Soc. 37 (1973), 47–49. MR 310048, DOI 10.1090/S0002-9939-1973-0310048-7
- Herbert Pahlings, Über die Kerne von Blöcken einer Gruppenalgebra, Arch. Math. (Basel) 25 (1974), 121–124 (German). MR 344326, DOI 10.1007/BF01238650
- È. M. Žmud′, On kernels of homomorphisms of linear representations of finite groups. , Mat. Sb. N.S. 44(86) (1958), 353–408 (Russian). MR 0098783
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 37-40
- MSC: Primary 20C05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0367042-1
- MathSciNet review: 0367042