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

theorem
  for G being finite Group,p being Prime
  for a being Element of G holds G is p-group & expon (G,p) = 2 &
  ord a = p |^2 implies G is commutative
proof
  let G be finite Group;
  let p be Prime;
  let a be Element of G;
  assume that
A1: G is p-group & expon (G,p) = 2 and
A2: ord a = p |^2;
  card G = p |^2 by A1,Def2;
  then G is cyclic by A2,GR_CY_1:19;
  hence thesis;
end;
