P-core-free iff there exists a faithful irreducible representation over a field of characteristic p

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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 G and a prime number p:

  1. G has no nontrivial normal p-subgroup.
  2. G possesses a faithful irreducible representation over a field of characteristic p.