theorem
  for H being strict Subgroup of G holds H * a = (0).G implies H = (0).G
proof
  let H be strict Subgroup of G;
  assume
A1: H * a = (0).G;
  then reconsider H as finite Subgroup of G by Th65;
  card (0).G = 1 by Th69;
  then card H = 1 by A1,Th64;
  hence thesis by Th70;
end;
