Geodesic
Some periodic groups admitting a finite regular automorphism of even order
Algebra i logika, Tome 58 (2019) no. 1, pp. 22-34.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the structure of an infinite group with automorphism of order $2p$ where $p$ is an odd prime leaving only the identity element fixed.
Keywords: periodic group, locally finite group
Mots-clés : Frobenius group, auto­morphism. 
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E. B. Durakov; A. I. Sozutov. Some periodic groups admitting a finite regular automorphism of even order. Algebra i logika, Tome 58 (2019) no. 1, pp. 22-34. http://geodesic.mathdoc.fr/item/AL_2019_58_1_a1/

[1] B. Fischer, “Finite groups admitting a fixed-point-free automorphism of order $2p$”, J. Algebra, 3:1 (1966), 99–114 | MR | Zbl

[2] V. Fischer, “Finite groups admitting a fixed-point-free automorphism of order $2p$. II”, J. Algebra, 5:1 (1967), 25–40 | MR | Zbl

[3] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985

[4] S. I. Adyan, Problema Bernsaida i tozhdestva v gruppakh, Nauka, M., 1975

[5] A. I. Sozutov, E. B. Durakov, “O tochno dvazhdy tranzitivnykh gruppakh s obobschenno konechnymi elementami”, Sib. matem. zh., 58:5 (2017), 1144–1149 | Zbl

[6] A. I. Sozutov, “O gruppakh s konechnym regulyarnym avtomorfizmom chetnogo poryadka”, Tez. dokl. mezhd. konf. “Aktualnye problemy prikladnoi matematiki i fiziki” (Kabardino-Balkarskaya resp., Prielbruse, Nalchik 17–21 maya 2017 g.), In-t prikl. matem. i avtomatizatsii KBNTs RAN, 2017, 193–194

[7] A. I. Sozutov, E. B. Durakov, Tez. dokl. Vserossiiskoi nauch. konf. “Algebra, analiz i smezhnye voprosy matematicheskogo modelirovaniya” (29 sentyabrya–1 oktyabrya 2017 g., g. Vladikavkaz), Sev.-Oset. gos. un-t im. K. L. Khetagurova, Vladikavkaz, 2017, 45

[8] A. M. Popov, A. I. Sozutov, V. P. Shunkov, Gruppy s sistemami frobeniusovykh podgrupp, IPTs KGTU, Krasnoyarsk, 2004

[9] X. Neiman, Mnogoobraziya grupp, Mir, M., 1969

[10] M. Kholl, Teoriya grupp, IL, M., 1962

[11] V. P. Shunkov, “Kharakterizatsiya nekotorykh konechnykh grupp Frobeniusa”, Matem. zametki, 43:6 (1988), 725–732

[12] V. P. Shunkov, “O parakh Frobeniusa vida $(F\lambda V, V)$”, Matem. sb., 180:10 (1989), 1311–1324

[13] V. M. Busarkin, Yu. M. Gorchakov, Konechnye rasscheplyaemye gruppy, Nauka, M., 1968

[14] A. I. Sozutov, A. K. Shlepkin, “O gruppakh s normalnoi komponentoi rasschepleniya”, Sib. matem. zh., 38:4 (1997), 897–914 | Zbl

[15] E.I. Khukhro, Nilpotentnye gruppy i ikh avtomorfizmy prostogo poryadka, Fraiburg, 1992

[16] V. A. Kreknin, A. I. Kostrikin, “Ob algebrakh Li s regulyarnym avtomorfizmom”, DAN SSSR, 149:2 (1963), 249–251 | Zbl

[17] D. Gorenstein, I. N. Herstein, “Finite groups admitting a fixed-point-free automorphism of order 4”, Am. J. Math., 83 (1961), 71–78 | MR | Zbl