Error in Wikipedia on a flipped $SO(10)$ model In the description of Wikipedia of flipped SO(10) model, it says that:

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*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

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*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.
 A: *

*Wiki "In flipped $SO(10)$ models, however, the gauge group is not just $SO(10)$ but $SO(10)_F  \times  U(1)_B$ or $[SO(10)_F \times U(1)_B]/\mathbf Z_4$." $\to$
My suggestion on the correction to a gauge group $Spin(10)$ but $Spin(10)_F \times U(1)_B$ or $[Spin(10)_F \times U(1)_B]/\mathbf Z_4$. This is because the $Spin(10)$ has a $\mathbf Z_4$ center.


*Wiki "If we suppose $[SU(5) \times U(1)_A]/\mathbf Z_5$ is a subgroup of $SO(10)_F$, then we have the intermediate scale symmetry breaking $[SO(10)_F \times U(1)_B]/\mathbf Z_4 \to [SU(5) \times U(1)_\chi]/\mathbf Z_5$"

This statement seems wrong. My suggestion on the correction to
$U(5) = [SU(5) \times U(1)_A]/\mathbf Z_5$ or $U(5)' = [SU(5) \times U(1)_\chi]/\mathbf Z_5$. $U(5)$ is a subgroup of $SO(10)$.
But $U(5)$ is not a subgroup of $Spin(10)$. Because we cannot lift the inclusion of $U(5)$ to $SO(10)$ to its double cover $Spin(10)$.
So we cannot have $[SU(5) × U(1)_A]/\mathbf Z_5$ as a subgroup of $Spin(10)_F$.
I think that $[Spin(10)_F × U(1)_B]/\mathbf Z_4$ does not contain U(5) = $[SU(5) \times U(1)_A]/\mathbf Z_5$ nor contain $U(5)' = [SU(5) \times U(1)_\chi]/\mathbf Z_5$ either as a subgroup. So the whole thing there does not work in this part.
Maybe other experts can comment.
