An f-subgroup is a linear recurring sequence subgroup, a multiplicative subgroup of a field whose elements can be generated (without repetition) by a linear recurrence relation, where the relation has characteristic polynomial f. It is called non-standard if it can be generated in a non-cyclic way (that is, not in the order ${\alpha }^i,{\alpha }^{i+1},{\alpha }^{i+2}\dots$ for a zero α of f), and standard otherwise. We will show that a finite f-subgroup is necessarily generated by a subset of the zeros of f. We use this result to improve on a recent theorem of Brison and Nogueira. A old question by Brison and Nogueira asks if there exist automatically non-standard f-subgroups, f-subgroups that cannot be generated by a zero of f. We answer that question affirmatively by constructing infinitely many examples.

一个F-亚组是线性的重复序列子组，一个字段，其元件可以被生成（不重复）的乘法子群由线性递归关系，其中该关系有特征多项式˚F。如果它可以以非循环方式生成（即，不是按顺序生成），则称为非标准${\alpha }^{\mathrm{一世}}，{\alpha }^{\mathrm{一世}+\mathrm{1个}}，{\alpha }^{\mathrm{一世}+\mathrm{2个}}\dots$对于零α的˚F），和标准物。我们将显示f的一个子集必然是由f的零个子集生成的。我们用这个结果来改进最近的Brison和Nogueira定理。通过布里森和诺盖拉甲老问题询问是否存在自动非标准f -subgroups，˚F不能通过的零来生成-subgroups ˚F。我们通过构建无限多个示例来肯定地回答该问题。