Some basic results on finite linear recurring sequence subgroups

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