theorem Th102:
  for H1,H2 being strict Subgroup of G holds H1,H2 are_conjugated
  iff ex g st H2 = H1 * g
proof
  let H1,H2 be strict Subgroup of G;
  thus H1,H2 are_conjugated implies ex g st H2 = H1 * g
  proof
    given g such that
A1: the addMagma of H1 = H2 * g;
    H1 * (-g) = H2 by A1,ThB62;
    hence thesis;
  end;
  given g such that
A2: H2 = H1 * g;
  H1 = H2 * (-g) by A2,ThB62;
  hence thesis;
end;
