On periodic groups saturated with a finite set of groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 321-326.

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

Let $G$ be a periodic group saturated with a finite set of groups of the form $L\times E$, where $E$ is a finite elementary abelian 2-group and $L$ is a finite simple non-abelian group, which is not isomorphic to $E_6(q)$, $^2E_6(q)$, $U_n(q)$ or $L_n(q)$ for odd $q$ and $n\geq 4$. We prove that $G$ is finite.
Keywords: Direct product of groups, periodic group
Mots-clés : saturation.
@article{SEMR_2014_11_a8,
     author = {I. V. Sabodakh},
     title = {On periodic groups saturated with a finite set of groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {321--326},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a8/}
}
TY  - JOUR
AU  - I. V. Sabodakh
TI  - On periodic groups saturated with a finite set of groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2014
SP  - 321
EP  - 326
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2014_11_a8/
LA  - ru
ID  - SEMR_2014_11_a8
ER  - 
%0 Journal Article
%A I. V. Sabodakh
%T On periodic groups saturated with a finite set of groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2014
%P 321-326
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2014_11_a8/
%G ru
%F SEMR_2014_11_a8
I. V. Sabodakh. On periodic groups saturated with a finite set of groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 321-326. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a8/

[1] A. K. Shlepkin, “Sopryazhenno biprimitivno konechnye gruppy, soderzhaschie konechnye nerazreshimye podgruppy”, Sb. tez. 3-i mezhdunar. konf. po algebre (Krasnoyarsk, 1993), 369

[2] A. A. Kuznetsov, K. A. Filippov, “Gruppy, nasyschennye zadannym mnozhestvom grupp”, Sibirskie elektronnye matematicheskie izvestiya, 8 (2011), 230–246 | MR

[3] A. K. Shlepkin, A. G. Rubashkin, “O gruppakh, nasyschennykh konechnym mnozhestvom grupp”, Sibirskii matematicheskii zhurnal, 45:6 (2004), 1397–1400 | MR | Zbl

[4] A. K. Shlepkin, A. G. Rubashkin, “O nekotorykh periodicheskikh gruppakh, nasyschennykh konechnymi prostymi gruppami”, Matem. sistemy, 2, Izd-vo KrasGAU, Krasnoyarsk, 2004, 96–100

[5] A. S. Kondratev, V. D. Mazurov, “2-signalizatory konechnykh prostykh grupp”, Algebra i logika, 42:5 (2003), 594–623 | MR

[6] D. V. Lytkina, L. R. Tukhvatullina, K. A. Filippov, “O periodicheskikh gruppakh, nasyschennykh konechnym mnozhestvom konechnykh prostykh grupp”, Sibirskii matematicheskii zhurnal, 49:2 (2008), 394–399 | MR | Zbl

[7] A. Kh. Zhurtov, “O regulyarnykh avtomorfizmakh poryadka 3 i parakh Frobeniusa”, Sibirskii matematicheskii zhurnal, 41:2 (2000), 329–338 | MR | Zbl

[8] V. V. Kabanov, A. S. Kondratev, Silovskie 2-podgruppy konechnykh grupp (obzor), IMM UNTs AN SSSR, Sverdlovsk, 1979 | Zbl

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

[10] L. Alperin, R. Brauer, D. Gorenstein, “Finite simple groups of 2-rank two”, Scripta Math., 29:3–4 (1973), 191–214 | MR | Zbl

[11] G. Glauberman, “Central elements in core-free groups”, J. Algebra, 4:3 (1966), 403–420 | DOI | MR | Zbl

[12] B. Huppert, Endliche Gruppen, v. I, Springer Verlag, 1979

[13] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Clarendon Press, 1985 | MR | Zbl