Geodesic
Bounded generation of Chevalley groups over rings of algebraic $S$-integers
Izvestiya. Mathematics , Tome 36 (1991) no. 1, pp. 101-128.

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

@article{IM2_1991_36_1_a4,
     author = {O. I. Tavgen'},
     title = {Bounded generation of {Chevalley} groups over rings of algebraic $S$-integers},
     journal = {Izvestiya. Mathematics },
     pages = {101--128},
     publisher = {mathdoc},
     volume = {36},
     number = {1},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a4/}
}
TY  - JOUR
AU  - O. I. Tavgen'
TI  - Bounded generation of Chevalley groups over rings of algebraic $S$-integers
JO  - Izvestiya. Mathematics 
PY  - 1991
SP  - 101
EP  - 128
VL  - 36
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a4/
LA  - en
ID  - IM2_1991_36_1_a4
ER  - 
%0 Journal Article
%A O. I. Tavgen'
%T Bounded generation of Chevalley groups over rings of algebraic $S$-integers
%J Izvestiya. Mathematics 
%D 1991
%P 101-128
%V 36
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a4/
%G en
%F IM2_1991_36_1_a4
O. I. Tavgen'. Bounded generation of Chevalley groups over rings of algebraic $S$-integers. Izvestiya. Mathematics , Tome 36 (1991) no. 1, pp. 101-128. http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a4/

[1] Base X., Milnor Dzh., Serr Zh.-P., “Reshenie kongruents-problemy dlya $\operatorname{SL}_n$ $(n\ge3)$”, Matematika, 14:6 (1970), 64–128; 15:1 (1971), 44–60

[2] James D., Waterhouse W., Weisfeiler B., “Abstract homomorphisms of algebraic groups: Problems and Bibliography”, Commun. Algebra., 9 (1981), 95–114 | DOI | MR | Zbl

[3] Carter D., Keller G., “Bounded elementary generation of $\operatorname{SL}_n(0)$”, Amer. J. Math., 105:3 (1983), 673–687 | DOI | MR | Zbl

[4] Matsumoto H., “Sur les sous-groupes arithmetiques des groupes semi-simples déployés”, Ann. scient. Ec. Norm. Sup. 4e série, 2 (1969), 1–62 | MR | Zbl

[5] Raghunathan M. S., A note on generators for arithmetic subgroups of algebraic group, Preprint, Tata Institute of fundamental research, Bombay, 1988 | MR

[6] Vasershtein L. N., “Stroenie klassicheskikh arifmeticheskikh grupp ranga, bolshego 1”, Matem. sb., 91:3 (1973), 445–470 | MR

[7] Zakiryanov K. X., “Konechnost shiriny simplekticheskikh grupp nad koltsami algebraicheskikh chisel otnositelno elementarnykh matrits”, Algebra i logika, 24:6 (1985), 667–673 | MR | Zbl

[8] Cooke G., Weinberger P., “On the construction of division chains in algebraic number rings, with applications to $\operatorname{SL}_2$”, Commun. Algebra, 3 (1975), 481–524 | DOI | MR | Zbl

[9] Raghunathan M. S., “On the congruence subgroup problem”, Publ. Math. IHES, 46 (1976), 107–161 | MR | Zbl

[10] Platonov V. P., “Koltsa i mnogoobraziya predstavlenii konechno porozhdennykh grupp”, Voprosy algebry, 4 (1988), 36–40

[11] Abe E., “Chevalley groups over local rings”, Tohoku Math. J., 21:3 (1969), 474–494 | DOI | MR | Zbl

[12] Abe E., “Coverings of twisted Chevalley groups over commutative rings”, Sci. Repts Tokyo Kyoiku Daigaku, A13:366–382 (1977), 194–218 | MR

[13] Suzuki K., “On normal subgroups of twisted Chevalley groups over local rings”, Sci. Repts Tokyo Kyoiku Daigaku, A13:366–382 (1977), 86–97 | MR

[14] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

[15] Borel A., “Svoistva i lineinye predstavleniya grupp Shevalle”, Seminar po algebraicheskim gruppam: Sb. statei, Mir, M., 1973 | MR | Zbl

[16] Deodhar V. V., “On central extensions of rational points of algebraic groups”, Amer. J. Math., 100:2 (1978), 303–386 | DOI | MR | Zbl

[17] Tits Zh., “Klassifikatsiya poluprostykh algebraicheskikh grupp”, Matematika, 12:2 (1968), 110–143 | MR

[18] Platonov V. P., “Arifmeticheskaya teoriya algebraicheskikh grupp”, Uspekhi matem. nauk, 37:3 (1982), 3–54 | MR | Zbl

[19] Burbaki N., Gruppy i algebry Li, Gl. IV–VI, Mir, M., 1972 | MR | Zbl

[20] Moy A., “Minimal $K$-types for $G_2$ over $p$-adic field”, Trans. Amer. Math. Soc., 305:2 (1988), 517–529 | DOI | MR | Zbl

[21] Seligman G., “On automorphisms of Lie algebras of classical type II”, Trans. Amer. Math. Soc., 94 (1960), 452–482 | DOI | MR | Zbl

[22] Burbaki N., Gruppy i algebry Li, Gl. VII, VIII, Mir, M., 1978 | MR

[23] Plotkin E. B., Setevye podgruppy grupp Shevalle i voprosy stabilizatsii $K_1$-funktora, Dis. ... kand. fiz.-matem. nauk, L., 1986

[24] Abe E., Suzuki K., “On normal subgroups of Chevalley groups over commutative rings”, Tohoku Math. J., 28:2 (1976), 185–198 | DOI | MR | Zbl

[25] Vavilov N. A., “O parabolicheskikh podgruppakh grupp Shevalle nad polulokalnym koltsom”, 3ap. nauchn. sem. LOMI, 75 (1978), 43–58 | MR | Zbl

[26] Magnus V., Karras A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974 | MR | Zbl

[27] Lazard M., “Groupes analytiques $p$-adiques”, Publ. Math. IHES., 26 (1965), 389–603 | MR | Zbl

[28] Dennis R. K., Vaserstein L. N., “On a question of M. Newman on the number of commutators”, J. Algebra, 118 (1988), 150–161 | DOI | MR | Zbl

[29] Carter D., Keller G., Bounded elementary expressions in $\operatorname{SL}(2,0)$, Preprint, 1985

[30] Grunewald F. J., Schwermer J., “Free non-abelian quotients of $\operatorname{SL}_2$ over orders of imaginary quadratic memberfields”, J. Algebra, 69:2 (1981), 298–304 | DOI | MR | Zbl