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Список литературы
|
|
|
1. |
Артин Э., Геометрическая алгебра, Наука, М., 1969 |
2. |
Вавилов Н. А., Петров В. А., “О надгруппах $\mathrm{EO}(2l,R)$”, Зап. науч. семин. ПОМИ, 272, 2000, 68–85 |
3. |
Вавилов Н. А., Петров В. А., “О надгруппах $\mathrm{Ep}(2l,R)$”, Алгебра и анализ, 15:4 (2003), 72–114 |
4. |
Вавилов Н. А., Петров В. А., “О надгруппах $\mathrm{EO}(n,R)$”, Алгебра и анализ, 19:2 (2007), 10–51 |
5. |
Вавилов Н. А., Степанов А. В., “Надгруппы полупростых групп”, Вестник СамГУ. Естественнонауч. сер., 2008, № 3, 51–95 |
6. |
Васерштейн Л. Н., “Стабилизация унитарных и ортогональных групп над кольцом с инволюцией”, Мат. сб., 81:3 (1970), 328–351 |
7. |
Васерштейн Л. Н., “Стабилизация для классических групп над кольцами”, Мат. сб., 93:2 (1974), 268–295 |
8. |
Голубчик И. З., “О нормальных делителях ортогональной группы над ассоциативным кольцом с инволюцией”, Успехи мат. наук, 30:6 (1975), 165 |
9. |
Петров В. А., “Нечётные унитарные группы”, Зап. науч. семин. ПОМИ, 305, 2003, 195–225 |
10. |
Суслин А. А., “О структуре специальной линейной группы над кольцами многочленов”, Изв. АН СССР. Сер. мат., 41:2 (1977), 235–252 |
11. |
Bak A., The stable structure of quadratic modules, Thesis, Columbia Univ., 1969 |
12. |
Bak A., $K$-Theory of forms, Ann. of Math. Stud., 98, Princeton Univ. Press, Princeton, NJ, 1982 |
13. |
Bak A., “Nonabelian $K$-theory: the nilpotent class of $K_1$ and general stability”, K-Theory, 4:4 (1991), 363–397 |
14. |
Bak A., Hazrat R., Vavilov N., “Localisation-completion strikes again: relative $K_1$ is nilpotent by abelian”, J. Pure Appl. Algebra, 213:6 (2009), 1075–1085 |
15. |
Bak A., Preusser R., “The E-normal structure of odd-dimensional unitary groups”, J. Pure Appl. Algebra, 222:9 (2018), 2823–2880 |
16. |
Bak A., Vavilov N., “Normality for elementary subgroup functors”, Math. Proc. Cambridge Philos. Soc., 118:1 (1995), 35–47 |
17. |
Bak A., Vavilov N., “Structure of hyperbolic unitary groups. I. Elementary subgroups”, Algebra Colloq., 7:2 (2000), 159–196 |
18. |
Bass H., “$K$-theory and stable algebra”, Publ. Math. Inst. Hautes Etudes Sci., 22 (1964), 5–60 |
19. |
Bass H., “Unitary algebraic $K$-theory”, Lecture Notes in Math., 342, Springer, Berlin, 1973, 57–265 |
20. |
Dieudonné J., On the automorphism of the classical groups, Mem. Amer. Math. Soc., 2, 1951, 1–122 pp. |
21. |
Dieudonné J., Sur les groupes classiques, Act. Sci. Industr., 1040, 3-eme ed., Hermann, Paris, 1973 |
22. |
Dieudonné J., La géometrie des groupes classiques, Ergeb. Math. Grenzgeb., 5, 3-eme ed., Springer Verlag, Berlin, 1971 |
23. |
Hahn A., O'Meara O. T., The classical groups and $K$-theory, Grundlehren Math. Wiss., 291, Springer-Verlag, Berlin, 1989 |
24. |
Hazrat R., “Dimension theory and nonstable $K_1$ of quadratic modules”, K-Theory, 27:4 (2002), 293–328 |
25. |
Hazrat R., Vavilov N., “Bak's work on the $K$-theory of rings”, J. K-Theory, 4:1 (2009), 1–65 |
26. |
Hong You, “Overgroups of symplectic groups in linear group over commutative rings”, J. Algebra, 282:1 (2004), 23–32 |
27. |
Hong You, “Overgroups of classical groups over commutative ring in linear group”, J. Algebra, 304:2 (2006), 1004–1013 |
28. |
Knus M.-A., Quadratic and hermitian forms over rings, Grundlehren Math. Wiss., 294, Springer-Verlag, Berlin, 1991 |
29. |
Li Fu An, “The structure of symplectic group over arbitrary commutative rings”, Acta Math. Sinica (N.S.), 3:3 (1987), 247–255 |
30. |
Li Fu An, “The structure of orthogonal groups over arbitrary commutative rings”, Chinese Ann. Math. Ser. B, 10:3 (1989), 341–350 |
31. |
Petrov V. A., “Overgroups of unitary groups”, K-Theory, 29:3 (2003), 147–174 |
32. |
Preusser R., “Structure of hyperbolic unitary groups II: classification of E-normal subgroups”, Algebra Colloq., 24:2 (2017), 195–232 |
33. |
Preusser R., “Sandwich classification for $\mathrm{GL}_n(R)$, $\mathrm O_{2n}(R)$ and $\mathrm U_{2n}(R, \Lambda)$ revisited”, J. Group Theory, 21:1 (2017), 21–44 |
34. |
Preusser R., “Sandwich classification for $O_{2n + 1}(R)$ and $U_{2n + 1}(R, \Delta)$ revisited”, J. Group Theory, 21:4 (2018), 539–571 |
35. |
Tang Guoping, “Hermitian groups and $K$-theory”, K-Theory, 13:3 (1998), 209–267 |
36. |
Tits J., “Formes quadratiques, groupes orthogonaux et algébres de Clifford”, Invent. Math., 5 (1968), 19–41 |
37. |
Vaserstein L., “Normal subgroups of orthogonal groups over commutative rings”, Amer. J. Math., 110:5 (1988), 955–973 |
38. |
Vaserstein L., “Normal subgroups of symplectic groups over rings”, K-Theory, 2:5 (1989), 647–673 |
39. |
Vaserstein L., You Hong, “Normal subgroups of classical groups over rings”, J. Pure Appl. Algebra, 105:1 (1995), 93–106 |
40. |
Vavilov N., “Intermediate subgroups in Chevalley groups”, Groups of Lie Type and their Geometries (Como, 1993), London Math. Soc. Lecture Note Ser., 207, Cambridge Univ. Press, Cambridge, 1995, 233–280 |
41. |
Wall C. T. C., “On the axiomatic foundation of the theory of Hermitian forms”, Proc. Cambridge. Phil. Soc., 67 (1970), 243–250 |
42. |
Weil A., “Algebras with involution and classical groups”, J. Indian Math. Soc. (N.S.), 24 (1961), 589–623 |
43. |
Wilson J., “The normal and subnormal structure of general linear groups”, Proc. Cambridge Philos. Soc., 71 (1972), 163–177 |