let p be natural prime number ; :: thesis: for G being finite strict Group st G is p -group & expon G,p = 0 holds
G = (1). G
let G be finite strict Group; :: thesis: ( G is p -group & expon G,p = 0 implies G = (1). G )
assume ( G is p -group & expon G,p = 0 ) ; :: thesis: G = (1). G
then A1: card G = p |^ 0 by def2
.= 1 by NEWTON:9 ;
card ((1). G) = 1 by GROUP_2:81;
hence G = (1). G by A1, GROUP_2:85; :: thesis: verum