Let be a subgroup of the three dimensional projective group defined over a finite field of order , viewed as a subgroup of where is an algebraic closure of . For and for the seven nonsporadic, maximal subgroups of , we investigate the (projective, irreducible) plane curves defined over that are left invariant by . For each, we compute the minimum degree of -invariant curves, provide a classification of all -invariant curves of degree , and determine the first gap in the spectrum of the degrees of all -invariant curves. We show that the curves of degree belong to a pencil depending on , unless they are uniquely determined by . For most examples of plane curves left invariant by a large subgroup of , the whole automorphism group of the curve is linear, i.e., a subgroup of . Although this appears to be a general behavior, we show that the opposite case can also occur for some irreducible plane curves, that is, the curve has a large group of linear automorphisms, but its full automorphism group is nonlinear.

中文翻译：

---

特征 p 中具有大线性自同构群的平面曲线

让 是在有限阶域上定义的三维射影群的子群，被视为 的子群，其中 是 的代数闭包。对于 和 的七个非零星最大子群，我们研究了在 上定义的（射影，不可约）平面曲线，该曲线由 保持不变。对于每一个，我们计算 不变曲线的最小次数，提供 次数的所有 不变曲线的分类，并确定所有 不变曲线的次数谱中的第一个间隙。我们表明，次数曲线属于铅笔，取决于 ，除非它们由 唯一确定。对于大多数由 的大子群保持不变的平面曲线示例，曲线的整个自同构群是线性的，即 的子群。虽然这看起来是一种普遍行为，但我们表明，对于一些不可约平面曲线也可能出现相反的情况，即曲线具有一大群线性自同构，但其完全自同构群是非线性的。