let p be Prime; :: thesis: for G being finite strict Group st G is p -group & expon (G,p) = 1 holds
G is p -commutative-group
let G be finite strict Group; :: thesis: ( G is p -group & expon (G,p) = 1 implies G is p -commutative-group )
assume A1: ( G is p -group & expon (G,p) = 1 ) ; :: thesis: G is p -commutative-group
then G is cyclic by Th25;
hence G is p -commutative-group by A1; :: thesis: verum