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- W3136280680 abstract "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, with characteristic polynomial $f$. It is called non-standard if it can be generated in a non-cyclic way (that is, not in the order $alpha^i, alpha^{i+1}, alpha^{i+2} ldots$ for a zero $alpha$ 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." @default.
- W3136280680 created "2021-03-29" @default.
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- W3136280680 date "2021-03-25" @default.
- W3136280680 modified "2023-09-27" @default.
- W3136280680 title "Some basic results on finite linear recurring sequence subgroups" @default.
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