Non-standard groups of the second type

Owen J. Brison, J. Eurico Nogueira

Research output: Contribution to journalArticlepeer-review


In [4] it is proved that the multiplicative group Fp⁎ is an automatically non-standard f-subgroup, here called a non-standard f-subgroup of the second type, for suitable f(x)∈Fp[x] whenever p is a prime with p>3 and p≡3(mod4). Here we extend this result to all odd non-Fermat primes p, and give two different proofs. Our first proof is an elaboration of that in [4], while the second proof leads to a general lower bound on the number of f-sequences that represent a non-standard f-subgroup of the second type; in certain very special cases, this lower bound is shown to be exact, although it is known not to be exact in general.
Original languageEnglish
Article number102302
Number of pages18
JournalFinite Fields And Their Applications
Early online date19 Sept 2023
Publication statusPublished - Dec 2023


  • Cyclotomic polynomial
  • Fermat prime
  • Finite field
  • Linear recurrence relation
  • Non-standard subgroup
  • Second type
  • Sophie-Germain prime


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