Groups with faithful blocks

Pahlings, H.

doi:10.1090/S0002-9939-1975-0367042-1

Groups with faithful blocks
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by H. Pahlings

Proc. Amer. Math. Soc. 51 (1975), 37-40

DOI: https://doi.org/10.1090/S0002-9939-1975-0367042-1

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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