P-core-free iff there exists a faithful irreducible representation over a field of characteristic p
From Groupprops
This article gives a proof/explanation of the equivalence of multiple definitions for the term p-core-free group
View a complete list of pages giving proofs of equivalence of definitions
Statement
The following are equivalent for a finite group and a prime number
:
-
has no nontrivial normal
-subgroup.
-
possesses a faithful irreducible representation over a field of characteristic
.