The general linear group is the set of Matrices with entries in the Field which have Nonzero Determinant.
See also Langlands Reciprocity, Projective General Linear Group, Projective Special Linear Group, Special Linear Group
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.
``The Groups , ,
.'' §2.1 in
Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England:
Clarendon Press, p. x, 1985.