  We consider the effect of glide-plane symmetry of the Fe-pnictogen/chalcogen
layer in Fe-based superconductors on pairing in spin fluctuation models. Recent
theories have proposed that so-called $\eta$-pairing states with nonzero total
momentum can be realized and possess exotic properties such as odd parity spin
singlet symmetry and time-reversal symmetry breaking. Here we show that $\eta$
pairing is inevitable when there is orbital weight at the Fermi level from
orbitals with even and odd mirror reflection symmetry in $z$; however, by
explicit calculation, we conclude that the gap function that appears in
observable quantities is identical to that found in earlier, 1 Fe per unit cell
pseudocrystal momentum calculations.
