let p be Prime; :: thesis: for G being finite strict Group st G is p -group & expon (G,p) = 1 holds
G is cyclic
let G be finite strict Group; :: thesis: ( G is p -group & expon (G,p) = 1 implies G is cyclic )
assume ( G is p -group & expon (G,p) = 1 ) ; :: thesis: G is cyclic
then card G = p |^ 1 by Def2
.= p ;
hence G is cyclic by GR_CY_1:21; :: thesis: verum