Two small and independent interrogative remarks:

(1) Nowadays, an extension of a group *G* by a group *K* is a group *H* fitting in a short exact sequence

in other words, and rather counterintuitively, the group *G *is a quotient of the group which is the extension. When did this terminology originate? A paper of Alan Turing (entitled, rather directly, “The extensions of a group”) defines “extension”, in the very first paragraph, exactly in the opposite (naïve) way, quoting Schreier and Baer who, presumably, had the same convention.

(2) There’s a whole lot of discussion here and there about the mystical “field with one element”; usually, papers of Tits from around 1954 are mentioned as being the source of the whole “idea”; however, the following earlier quote from a 1951 paper of R. Steinberg (“A geometric approach to the representations of the full linear group over a Galois field”, 1951, p. 279, TAMS 71, 274–282) seems to also contain a germ of the often mentioned analogy between the formulas for the order of the Weyl groups and those of groups of Lie type over a field with *q *elements, the former being obtained by specializing the latter for *q=1*:

In closing this section, a remark on the analogy between

GandHseems to be in order. Instead of consideringGas a group of linear transformations of a vector space, we could considerGas a collineation group of a finite(n-1)-dimensional geometry. Ifq=1, the vector space fails to exist but the finite geometry does exist and, in fact, reduces to thenvertices of a simplex with a collineation group isomorphic toH. “

In this citation, *G *is *GL(n, F_{q})*, and

*H*is the symmetric group on

*n*letters.

(3) Here’s a third question: when did the terminology “Galois field” become more or less obsolete within the pure mathematics community?