Section FrobeniusProperties.
Variables G H K : {group gT}.
Hypothesis frobG : [Frobenius G = K ><| H].
End FrobeniusProperties.

Lemma prime_FrobeniusP G K H :
K :!=: 1 -> prime #|H| ->
reflect (K ><| H = G /\ 'C_K(H) = 1) [Frobenius G = K ><| H].