Automorphisms of stable linear groups over commutative local rings with~$1/2$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 15-30.

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In the paper, we describe automorphisms of stable linear groups $\mathrm E(R)$ and $\mathrm{GL}(R)$ over commutative local rings $R$ with $1/2$.
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A. S. Atkarskaya. Automorphisms of stable linear groups over commutative local rings with~$1/2$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 15-30. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a1/

[1] Golubchik I. Z., Lineinye gruppy nad assotsiativnymi koltsami, Dis. $\dots$ dokt. fiz.-mat. nauk, Ufa, 1997

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

[3] Zelmanov E. I., “Izomorfizmy lineinykh grupp nad assotsiativnym koltsom”, Sib. mat. zhurn., 26:4 (1985), 49–67 | MR | Zbl

[4] Petechuk V. M., “Avtomorfizmy matrichnykh grupp nad kommutativnymi koltsami”, Mat. sb., 117(159):4 (1982), 534–547 | MR | Zbl

[5] Pomfre Zh., Makdonald B., “Avtomorfizmy $\mathrm{GL}_n(R)$, $R$ – lokalnoe koltso”, Avtomorfizmy klassicheskikh grupp, Mir, M., 1976, 176–187

[6] Dieudonne J., “On the automorphisms of the classical groups”, Mem. Am. Math. Soc., 2 (1951), 1–95 | DOI | MR

[7] Hahn A. J., O'Meara O. T., The Classical Groups and K-Theory, Springer, Berlin, 1989 | MR | Zbl

[8] Hua L. K., Reiner I., “Automorphisms of the unimodular group”, Trans. Am. Math. Soc., 71 (1951), 331–338 | DOI | MR

[9] Landin J., Reiner I., “Automorphisms of the general linear group over a principal ideal domain”, Ann. Math., 65:3 (1957), 519–526 | DOI | MR | Zbl

[10] O'Meara O., Lectures on Linear Groups, Providence, Rhode Island, 1974

[11] Rickart C. E., “Isomorphic group of linear transformations. I”, Am. J. Math., 72 (1950), 451–464 | DOI | MR | Zbl

[12] Schreier O., van der Waerden B. L., “Die Automorphismen der projektiven Gruppen”, Abh. Math. Sem. Univ. Hamburg, 6 (1928), 303–322 | DOI | MR | Zbl

[13] Wan C. A., “An the automorphism of linear group over a noncommutative principal ideal domain of characteristic $\neq2$”, Acta Math. Sinica, 7 (1957), 533–573 | MR

[14] Waterhouse W. C., “Automorphisms of $\mathrm{GL}_n(R)$”, Proc. Am. Math. Soc., 79:3 (1980), 347–351 | MR | Zbl

[15] Shi-Jian Yan, “Linear groups over a ring”, Chinese Math., 7:2 (1965), 163–179 | MR