theorem Th105:
  for H1,H2 being strict Subgroup of G holds H1,H2 are_conjugated
  & H2,H3 are_conjugated implies H1,H3 are_conjugated
proof
  let H1,H2 be strict Subgroup of G;
  given g such that
A1: the addMagma of H1 = H2 * g;
  given h such that
A2: the addMagma of H2 = H3 * h;
  H1 = H3 * (h + g) by A1,A2,Th60;
  hence thesis;
end;
