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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 13th 2019

some minimum, for cross-linking with Sp(n).Sp(1)

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 13th 2019

changed page name to singular

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 16th 2019
• (edited May 16th 2019)

When I started this entry, I deliberately changed the wording of the definition as compared to what one finds in most of the literature.

I have added now a remark on this point, for clarity:

Beware that most texts insists on stating the choices in the definition of the central product as that of

Beware that most texts insists on stating the choices in Def. \ref{CentralProduct} as that of

1. two separate subgroups $C_i \xhookrightarrow{\iota_i} Z(G_i)$

2. an isomorphism $C_1 \xrightarrow[\simeq]{\phi} C_2$ between them

and insists that the second group acts via $(-)^{-1}\circ \phi$.

These clauses matter if one thinks of the subgroup inclusions as in material set theory. But we speak structural set theory, which means that a subgroup inclusion as in (eq:SubgroupInclusion) is really a choice of monic homomorphism, and this choice already absorbs the choice of $\phi$ and or $(-)^{-1}\circ \phi$ above.