Geodesic
Some properties of elements of the prime field
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 60-68.

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We obtain some properties of primitive roots in the groups of residue class modulo prime number, in particular, Fermat primes and Sophie Germain primes. We also obtain some formulas for computation of products of elements in some subsets of the prime field of positive characteristic.
Keywords: prime field
Mots-clés : Fermat primes, Sophie Germain primes. 
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S. A. Tyurin. Some properties of elements of the prime field. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 60-68. http://geodesic.mathdoc.fr/item/IVM_2016_8_a5/

[1] Kostrikin A. I., Shafarevich I. R., “Graduirovannye algebry Li konechnoi kharakteristiki”, Izv. AN SSSR. Ser. matem., 33:2 (1969), 251–322 | MR | Zbl

[2] Demushkin S. P., “Podalgebry Kartana prostykh neklassicheskikh $p$-algebr Li”, Izv. AN SSSR. Ser. matem., 36:4 (1972), 915–932 | MR | Zbl

[3] Wilson R. L., “Cartan subalgebras and tori in prime characteristic”, Proc. Amer. Math. Soc., 53:2 (1975), 325–327 | DOI | MR | Zbl

[4] Tyurin S. A., “O podalgebrakh Kartana obschei algebry Li kartanovskogo tipa”, Matem. sb., 116(158):4 (1981), 547–557 | MR | Zbl

[5] Barnes D. W., “On Cartan subalgebras of Lie algebras”, Math. Z., 101 (1967), 350–355 | DOI | MR | Zbl

[6] Wilson R. L., “Automorphisms of graded Lie algebras of Cartan type”, Comm. Algebra, 3:7 (1975), 591–613 | DOI | MR | Zbl

[7] Tyurin S. A., “Klassifikatsiya torov v algebre Tsassenkhauza”, Izv. vuzov. Matem., 1998, no. 2, 69–76 | MR | Zbl

[8] Tyurin S. A., “Nekotorye tipy differentsialnykh uravnenii nad polem konechnoi kharakteristiki”, Izv. vuzov. Matem., 1992, no. 1, 81–83 | MR | Zbl

[9] Tyurin S. A., “Modulyarnaya trigonometriya”, Nelineinyi mir, 6:11–12 (2008), 704–712

[10] Tyurin S. A., “Simvol tipa i teorema Vilsona”, Izv. vuzov. Matem., 2012, no. 9, 47–53 | MR | Zbl