In the description of Wikipedia of flipped SO(10) model, it says that:
In flipped $SO(10)$ models, however, the gauge group is $[SO(10)_F × U(1)_B]/Z_4$.
If we suppose $[SU (5) × U(1)_χ ]/ Z_5$ is a subgroup of $SO(10)_F$, then we have the intermediate scale symmetry breaking $[SO(10)_F × U(1)_B]/Z_5 → [ SU(5) × U(1)_χ]/Z_5$ where $\chi=-{A\over 4}+{5B\over 4}$.
My question is that
should $[SO(10)_F × U(1)_B]/Z_4$ and $[SO(10)_F × U(1)_B]/Z_5$ mentioned above, they are the same group or not? Is that one of them has a typo and indeed are the same as $[SO(10)_F × U(1)_B]/Z_4$?
What exactly are the $A$ and $B$ in $\chi=-{A\over 4}+{5B\over 4}$? I think that $B$ stands for a $U(1)$, and $B$ does not imply baryon, correct? But $A$ does not show up anywhere on the Wikipedia page.