Abstract:Let G be a subgroup of the three dimensional projective group PGL(3, q) defined over a finite field Fq of order q, viewed as a subgroup of PGL(3, K) where K is an algebraic closure of Fq. For the seven nonsporadic, maximal subgroups G of PGL(3, q), we investigate the (projective, irreducible) plane curves defined over K that are left invariant by G. For each, we compute the minimum degree d(G) of Ginvariant curves, provide a classification of all G-invariant curves of degree d(G), and determine the first gap ε… Show more
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