General Linear Group

The general linear group ${\it GL}_n(q)$ is the set of $n\times n$ Matrices with entries in the Field $\Bbb{F}_q$ which have Nonzero Determinant.

See also Langlands Reciprocity, Projective General Linear Group, Projective Special Linear Group, Special Linear Group

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``The Groups ${\it GL}_n(q)$, ${\it SL}_n(q)$, ${\it PGL}_n(q)$, and ${\it PSL}_n(q)={\it L}_n(q)$.'' §2.1 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.