  In this work, we analyze the nonsymmorphic symmetry group structures for a
variety of generalized Kitaev spin chains and ladders with bond alternations,
including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond nearest
neighbor interactions, and two-leg spin ladders. The symmetry analysis is
applied to determine the symmetry breaking patterns of several magnetically
ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the
dimerization order parameters for spontaneous dimerizations. Our work is useful
in understanding the magnetic phases in related models and may provide guidance
for the symmetry classifications of mean field solutions in further
investigations.
