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The article pin group says
The Pin group Pin(V;q) of a quadratic vector space, def. 2.1, is the subgroup of the group of units in the Clifford algebra Cl(V,q) Pin(V,q)↪GL 1(Cl(V,q)) on those elements which are multiples v_1 \cdots v_{2k} of elements v_i \in V with q(V) = 1.
It appears that this defines the spin group, not the pin group, because 2k is even. For the pin group one needs to allow an arbitrary number of v_i.
The same problem seems to be present in the article spin group.
Thanks for catching. Fixed now (both entries). Also fixed the typo right afterwards, (capital $V$ to lower case).
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