Automorphisms of Chevalley groups of types $B_2$ and $G_2$ over local rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 4, pp. 3-29.

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In the paper, we prove that every automorphism of any adjoint Chevalley group of type $B_2$ or $G_2$ is standard, i.e., it is a composition of an “inner” automorphism, a ring automorphism, and a central automorphism.
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E. I. Bunina. Automorphisms of Chevalley groups of types $B_2$ and $G_2$ over local rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 4, pp. 3-29. http://geodesic.mathdoc.fr/item/FPM_2007_13_4_a0/

[1] Abe E., “Avtomorfizmy grupp Shevalle nad kommutativnymi koltsami”, Algebra i analiz, 5:2 (1993), 74–90 | MR | Zbl

[2] Bunina E. I., “Avtomorfizmy prisoedinënnykh grupp Shevalle tipov $A_l$, $D_l$, $E_l$ nad lokalnymi koltsami”, Uspekhi mat. nauk, 62:5 (2007), 143–144 | MR | Zbl

[3] Burbaki N., Gruppy i algebry Li. Gruppy Kokstera i sistemy Titsa, gruppy, porozhdënnye otrazheniyami, sistemy kornei, Mir, M., 1972 | MR | Zbl

[4] Golubkov A. Yu., Pervichnyi radikal klassicheskikh grupp nad assotsiativnymi koltsami, Dis. ... kand. fiz.-mat. nauk, M., 2001

[5] Golubchik I. Z., Mikhalëv A. V., “Izomorfizmy obschei lineinoi gruppy nad assotsiativnym koltsom”, Vestn. Mosk. un-ta. Ser. 1, Matematika, mekhanika, 1983, no. 3, 61–72 | MR | Zbl

[6] Petechuk V. M., “Avtomorfizmy grupp $\operatorname{SL}_n$, $\operatorname{GL}_n$ nad nekotorymi lokalnymi koltsami”, Mat. zametki, 28:2 (1980), 187–206 | MR

[7] Petechuk V. M., “Avtomorfizmy grupp $\operatorname{SL}_3(K)$, $\operatorname{GL}_3(K)$”, Mat. zametki, 31:5 (1982), 657–668 | MR | Zbl

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

[9] Suslin A. A., “Odna teorema Kona”, Zap. nauch. sem. LOMI AN SSSR, 64 (1976), 127–130 | MR | Zbl

[10] Khamfris Dzh., Vvedenie v teoriyu algebr Li i ikh predstavlenii, MTsNMO, M., 2003

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

[12] Abe E., Suzuki K., “On normal subgroups of Chevalley groups over commutative rings”, Tôhoku Math. J., 28:1 (1976), 185–198 | DOI | MR | Zbl

[13] Chevalley C., “Certains schémas de groupes semi-simples”, Sem. Bourbaki, 219, 1960/1961, 1–16 | MR

[14] Cohn P., “On the structure of the $\operatorname{GL}_2$ of a ring”, Inst. Hautes Études Sci. Publ. Math., 30 (1966), 365–413 | DOI | MR | Zbl

[15] Dieudonné J., On the Automorphisms of Classical Groups, Mem. Amer. Math. Soc. 2, 8, Amer. Math. Soc., 1951 | MR

[16] Hua L. K., Reiner I., “Automorphisms of unimodular groups”, Trans. Amer. Math. Soc., 71 (1951), 331–348 | DOI | MR | Zbl

[17] Humphreys J. F., “On the automorphisms of infinite Chevalley groups”, Can. J. Math., 21 (1969), 908–911 | DOI | MR | Zbl

[18] Matsumoto H., “Sur les sous-groupes arithmétiques des groupes semi-simples deployés”, Ann. Sci. École Norm. Sup., 2 (1969), 1–62 | MR | Zbl

[19] McDonald B. R., “Automorphisms of $\operatorname{GL}_n(R)$”, Trans. Amer. Math. Soc., 215 (1976), 145–159 ; 246 (1978), 155–171 | DOI | MR | Zbl | DOI | MR | Zbl

[20] O'Meara O. T., “The automorphisms of linear groups over any integral domain”, J. Reine Angew. Math., 223 (1966), 56–100 | DOI | MR

[21] Stein M. R., “Surjective stability in dimension 0 for $K_2$ and related functors”, Trans. Amer. Math. Soc., 178:1 (1973), 165–191 | DOI | MR | Zbl

[22] Steinberg R., “Automorphisms of finite linear groups”, Can. J. Math., 121 (1960), 606–615 | DOI | MR

[23] Suzuki K., “On the automorphisms of Chevalley groups over $p$-adic integer rings”, Kumamoto J. Sci. (Math.), 16:1 (1984), 39–47 | MR | Zbl

[24] Swan R., “Generators and relations for certain special linear groups”, Adv. Math., 6 (1971), 1–77 | DOI | MR | Zbl

[25] Vavilov N. A., Plotkin E. B., “Chevalley groups over commutative rings. I. Elementary calculations”, Acta Appl. Math., 45 (1996), 73–113 | DOI | MR | Zbl