Editing Projective linear group (section)

=== History ===
The groups {{nowrap|PSL(2, ''p'')}} for any prime number p were constructed by [[Évariste Galois]] in the 1830s, and were the second family of finite [[simple group]]s, after the [[alternating group]]s.<ref name="raw">{{Citation | last1=Wilson | first1=Robert A. | author-link = Robert Arnott Wilson | title=The finite simple groups | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=[[Graduate Texts in Mathematics]] 251 | isbn=978-1-84800-987-5 | doi=10.1007/978-1-84800-988-2 | zbl=1203.20012 | year=2009 |chapter = Chapter 1: Introduction |chapter-url=http://www.maths.qmul.ac.uk/~raw/fsgs_files/intro.ps | postscript = [www.maths.qmul.ac.uk/~raw/fsgs.html 2007 preprint] | volume=251}}</ref> Galois constructed them as fractional linear transforms, and observed that they were simple except if ''p'' was 2 or 3; this is contained in his last letter to Chevalier.<ref name="chevalier-letter">{{Citation| last = Galois | first = Évariste| year = 1846 | title = Lettre de Galois à M. Auguste Chevalier | journal = [[Journal de Mathématiques Pures et Appliquées]] | volume = XI | pages = 408–415 | url = http://visualiseur.bnf.fr/ark:/12148/cb343487840/date1846 | access-date = 2009-02-04 | postscript =, {{nowrap|PSL(2, ''p'')}} and simplicity discussed on p. 411; exceptional action on 5, 7, or 11 points discussed on pp. 411–412; {{nowrap|GL(''ν'', ''p'')}} discussed on p. 410}}</ref> In the same letter and attached manuscripts, Galois also constructed the [[General linear group#Over finite fields|general linear group over a prime field]], {{nowrap|GL(''ν'', ''p'')}}, in studying the Galois group of the general equation of degree ''p''<sup>''ν''</sup>.

The groups {{nowrap|PSL(''n'', ''q'')}} (general ''n'', general finite field) for any prime power ''q'' were then constructed in the classic 1870 text by [[Camille Jordan]], ''[[List of important publications in mathematics#Trait.C3.A9 des substitutions et des .C3.A9quations alg.C3.A9briques|Traité des substitutions et des équations algébriques]].''