reserve G for Group,
  a,b for Element of G,
  m, n for Nat,
  p for Prime;

theorem Th27:
  (1).G is p-commutative-group-like
  proof
    let a,b be Element of (1).G;
A1: the carrier of (1).G = {1_G} by GROUP_2:def 7;
    hence (a * b) |^ p = 1_G by TARSKI:def 1
    .= a |^ p * (b |^ p) by A1,TARSKI:def 1;
  end;
