# Talk:Galois geometry

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## Desarguesian spaces

I reverted the good faith edit which stated that Galois geometries are usually called finite Desarguesian spaces. This is not a true statement. Only in two dimensions is there a need to distinguish Desarguesian planes from other projective planes. As soon as the dimension gets to be three or more Desargues theorem is automatic and there is no reason talk about Desarguesian spaces, as every projective space is Desarguesian. Also, the term Galois geometry has always been applied to geometries defined over fields (especially finite ones) whereas the Desarguesian geometries are defined over skewfields and it just happens that the finite skewfields are fields, this is not true in the infinite case, so there is some reason to keep the terms seperate. And while I'm at it, the article makes it sound like Thas and Hirschfeld invented the term "Galois geometry" - this implication would embarass them both. The term, as far as I know, comes from the Italian school of geometers. Most likely B. Segre is responsible, but that is only a guess. Bill Cherowitzo (talk) 04:25, 15 September 2012 (UTC)

## Geometry with GF(3)

The following article uses PG(3,3), PG(4,3), and PG(5,3):

Does not this then constitute an application of Galois geometry. Entry of Tutte–Coxeter graph in § See also was reverted. — Rgdboer (talk) 20:21, 27 January 2018 (UTC)

There are a zillion graphs that can be embedded in Galois geometries, so why is this one being singled out? This might be more appropriate in a section on applications, but it doesn't shed any more light on what Galois geometries are, so it doesn't belong in a See also section. --Bill Cherowitzo (talk) 03:50, 28 January 2018 (UTC)