Geodesic
The structure of an infinite Sylow subgroup in some periodic Shunkov groups
Diskretnaya Matematika, Tome 14 (2002) no. 4, pp. 133-152.

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We study periodic groups such that the normaliser of any finite non-trivial subgroup of such a group is almost layer-finite. The class of groups satisfying this condition is rather wide and includes the free Burnside groups of odd period which is greater than 665 and the groups constructed by A. Yu. Olshanskii. We consider the classical question: how the properties of the system of subgroups of a group influence on the properties of the group? We show that almost layer-finiteness is transferred on the group $G$ from the normalisers of non-trivial finite subgroups of the group $G$ if $G$ is periodic conjugately biprimitively finite group with a strongly embedded subgroup. We study the structure of an infinite Sylow 2-subgroup in a periodic conjugately biprimitively finite group in the case that the normaliser of any finite non-trivial subgroup is almost layer-finite. The results of the paper can be useful in the study of the class of periodic conjugately biprimitively finite groups (periodic Shunkov groups). The research was supported by the Russian Foundation for Basic Research, grants 99–01–00432 and 02–01–00078, and by grant №9 of the Sixth Competition of Scientific Projects of Young Researchers in 1999. 
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V. I. Senashov. The structure of an infinite Sylow subgroup in some periodic Shunkov groups. Diskretnaya Matematika, Tome 14 (2002) no. 4, pp. 133-152. http://geodesic.mathdoc.fr/item/DM_2002_14_4_a5/

[1] Chernikov S. N., “K teorii beskonechnykh $p$-grupp”, Dokl. AN SSSR, 50 (1945), 71–74 | Zbl

[2] Adyan S. I., Problema Bernsaida i tozhdestva v gruppakh, Nauka, Moskva, 1975 | MR | Zbl

[3] Olshanskii A. Yu., Geometriya opredelyayuschikh sootnoshenii v gruppe, Nauka, Moskva, 1989 | MR

[4] Senashov V. I., “Gruppy s usloviem minimalnosti dlya ne pochti sloino konechnykh grupp”, Ukr. matem. zhurn., 43:7-8 (1991), 1002–1008 | MR

[5] Senashov V. I., “Pochti sloinaya konechnost periodicheskoi gruppy bez involyutsii.”, Ukr. matem. zhurn., 51:11 (1999), 1529–1533 | MR | Zbl

[6] Shunkov V. P., “O periodicheskikh gruppakh s pochti regulyarnoi involyutsiei”, Algebra i logika, 11:4 (1972), 470–493 | Zbl

[7] Chernikov S. N., Gruppy s zadannymi svoistvami sistemy podgrupp, Nauka, Moskva, 1980 | MR

[8] Shunkov V. P., “O lokalno konechnykh gruppakh konechnogo ranga”, Algebra i logika, 10:2 (1971), 199–225 | Zbl

[9] Shafiro A. A., Shunkov V. P., “Kharakterizatsiya beskonechnoi chernikovskoi gruppy, ne yavlyayuscheisya konechnym rasshireniem kvazitsiklicheskoi gruppy”, Matem. sb., 107(149):2(10) (1978), 289–303 | MR | Zbl

[10] Kargapolov M. I., “Lokalno konechnye gruppy, obladayuschie normalnymi sistemami s konechnymi faktorami”, Sib. matem. zhurn., 2:6 (1961), 853–873 | MR | Zbl

[11] Sozutov A. I., Shunkov V. P., “Ob odnom obobschenii teoremy Frobeniusa na beskonechnye gruppy”, Matem. sb., 100:4 (1976), 495–508 | MR

[12] Suchkova N. G., Shunkov V. P., “O gruppakh s usloviem minimalnosti dlya abelevykh podgrupp”, Algebra i logika, 26:4 (1986), 445–469 | MR

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

[14] Sozutov A. I., Shunkov V. P., “O beskonechnykh gruppakh, nasyschennykh frobeniusovymi podgruppami”, Algebra i logika, 16:6 (1977), 711–735 | MR | Zbl

[15] Brauer R., Suzuki M., “On finite groups with an abelian Sylow subgroups”, Canad. J. Math., 14 (1962), 436–450 | MR | Zbl

[16] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, Moskva, 1982 | MR | Zbl

[17] Hartley B.,, “Finite groups of automrphisms of locally soluble groups”, J. Algebra, 57:1 (1979), 242–257 | DOI | MR | Zbl

[18] Kegel O. H., Wehrfritz B. A. F., Locally finite groups, North-Holland, Amsterdam, 1973 | MR | Zbl

[19] Shunkov V. P., $M_p$-gruppy, Nauka, Moskva, 1990 | MR | Zbl

[20] Shunkov V. P., “Kharakterizatsiya pochti sloino konechnykh grupp v klasse lokalno konechnykh grupp”, Teoriya grupp, VTs SO RAN, Krasnoyarsk, 1996, 25—32

[21] Shunkov V. P., “O periodicheskikh gruppakh s nekotorymi usloviyami konechnosti”, Dokl. AN SSSR, 195:6 (1970), 1290–1293 | Zbl

[22] Shunkov V. P., O vlozhenii primarnykh elementov v gruppe, Nauka, Novosibirsk, 1992 | MR | Zbl