A description of the subgroups of the complete linear group that contain the group of diagonal matrices
Z. I. Borevich

This publication is cited in the following articles:

1. Eugene Plotkin, “Nikolai Vavilov, mathematics and life”, European Journal of Mathematics, 11:3 (2025)  
2. R. Yu. Dryaeva, “O nadgruppakh tsikla, bogatykh transvektsiyami”, Vladikavk. matem. zhurn., 26:1 (2024), 100–105    
3. Bui Xuan Hai, “On the Diagonal Subgroup of the Special Linear Group Over a Division Ring”, Acta Math Vietnam, 2024  
4. Gunnar Fløystad, “Surprising occurrences of order structures in mathematics”, JCD, 2024  
5. E. B. Plotkin, A. I. Generalov, N. S. Geldkhauzer, N. L. Gordeev, A. Yu. Luzgarev, V. V. Nesterov, I. A. Panin, V. A. Petrov, S. Yu. Pilyugin, A. V. Stepanov, A. K. Stavrova, V. G. Khalin, “O Nikolae Aleksandroviche Vavilove”, Voprosy teorii predstavlenii algebr i grupp. 40, Posvyaschaetsya pamyati Nikolaya Aleksandrovicha VAVILOVA, Zap. nauchn. sem. POMI, 531, POMI, SPb., 2024, 7–40  
6. N. Vavilov, V. Nesterov, “Podgruppy, porozhdennye paroi $2$-torov v $\mathrm{GL}(5,K)$”, Voprosy teorii predstavlenii algebr i grupp. 39, Zap. nauchn. sem. POMI, 522, POMI, SPb., 2023, 8–45  
7. V. V. Nesterov, “Izvlechenie malorangovykh unipotentnykh elementov v $\mathrm{SO}(2\ell,K)$”, Voprosy teorii predstavlenii algebr i grupp. 39, Zap. nauchn. sem. POMI, 522, POMI, SPb., 2023, 101–112  
8. N. A. Vavilov, “Saint Petersburg School of the Theory of Linear Groups. I. Prehistory”, Vestnik St.Petersb. Univ.Math., 56:3 (2023), 273  
9. N. A. Vavilov, “Sankt-Peterburgskaya shkola teorii lineinykh grupp. I. Predystoriya”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 10:3 (2023), 381–405    
10. V. Nesterov, “Extraction of Small Rank Unipotent Elements in GL(4, K)”, J Math Sci, 264:1 (2022), 86  
11. N. A. Dzhusoeva, S. S. Ikaev, V. A. Koibaev, “O podgruppakh, bogatykh transvektsiyami”, Vladikavk. matem. zhurn., 23:4 (2021), 50–55    
12. V. V. Nesterov, “Izvlechenie malorangovykh unipotentnykh elementov v $\mathrm{GL}(4,K)$”, Voprosy teorii predstavlenii algebr i grupp. 35, Zap. nauchn. sem. POMI, 492, POMI, SPb., 2020, 134–148  
13. A. V. Shchegolev, “Overgroups of elementary block-diagonal subgroups in the classical symplectic group over an arbitrary commutative ring”, St. Petersburg Math. J., 30:6 (2019), 1007–1041          
14. A. V. Shchegolev, “Overgroups of elementary block-diagonal subgroups in hyperbolic unitary groups over quasi-finite rings: main results”, J. Math. Sci. (N. Y.), 222:4 (2017), 516–523      
15. N. A. Dzhusoeva, “Set i elementarnaya setevaya gruppa, assotsiirovannye s nerasschepimym maksimalnym torom”, Vladikavk. matem. zhurn., 17:2 (2015), 12–15  
16. V. I. Yanchevskii, D. G. Medvedev, A. E. Zalesskii, V. I. Sarvanov, “Dmitrii Alekseevich Suprunenko: k 100-letiyu so dnya rozhdeniya”, Tr. In-ta matem., 23:2 (2015), 3–10  
17. N. A. Dzhusoeva, V. A. Koibaev, “Normalizer of an elementary net group associated with a non-split torus in the general linear group over a field”, J. Math. Sci. (N. Y.), 209:4 (2015), 549–554      
18. N. A. Dzhusoeva, “Ob izvlechenii transvektsii v nadgruppakh nerasschepimogo maksimalnogo tora”, Vladikavk. matem. zhurn., 15:1 (2013), 14–17  
19. Ya. N. Nuzhin, “Lie rings defined by the root system and family of additive subgroups of the main ring”, Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 119–125        
20. A. V. Shilov, “Koltso, opredelyayuschee strukturu nadgrupp nerasschepimogo maksimalnogo tora”, Vladikavk. matem. zhurn., 13:2 (2011), 63–66  
21. Yakov N. Nuzhin, “Faktorizatsiya kovrovykh podgrupp grupp Shevalle nad kommutativnymi koltsami”, Zhurn. SFU. Ser. Matem. i fiz., 4:4 (2011), 527–535  
22. V. A. Koibaev, A. V. Shilov, “On subgroups of the general linear group containing a non-split maximal torus”, J. Math. Sci. (N. Y.), 171:3 (2010), 380–385    
23. N. A. Dzhusoeva, V. S. Dzigoeva, V. A. Koibaev, “O maksimalnykh podgruppakh polnoi lineinoi gruppy nad polem ratsionalnykh funktsii”, Vladikavk. matem. zhurn., 12:4 (2010), 12–14  
24. N. Vavilov, “Weight elements of Chevalley groups”, St. Petersburg Math. J., 20:1 (2009), 23–57            
25. N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948          
26. V. A. Koibaev, “A group acting on the triangle nets”, J. Math. Sci. (N. Y.), 151:3 (2008), 3016–3017    
27. N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004          
28. N. Vavilov, “Geometry of 1-tori in $\mathrm{GL}(n,T)$”, St. Petersburg Math. J., 19:3 (2008), 407–429            
29. E. V. Dybkova, “Overgroups of the diagonal group in the hyperbolic unitary group over a simple Artin ring”, J. Math. Sci. (N. Y.), 145:1 (2007), 4781–4789        
30. E. V. Dybkova, “The theorem of Borewich for the hyperbolic unitary group over a skew field”, J. Math. Sci. (N. Y.), 136:3 (2006), 3908–3925        
31. K. Yu. Lavrov, “Subgroups of the orthogonal groups of even degree over a local field”, J. Math. Sci. (N. Y.), 136:3 (2006), 3966–3971        
32. E. V. Dybkova, “Overdiagonal subgroups of the hyperbolic unitary group for the good form ring over a skew field”, J. Math. Sci. (N. Y.), 130:3 (2005), 4712–4719        
33. Michael Schmid, Rainer Steinwandt, Jörn Müller-Quade, Martin Rötteler, Thomas Beth, “Decomposing a matrix into circulant and diagonal factors”, Linear Algebra and its Applications, 306:1-3 (2000), 131  
34. E. V. Dybkova, “Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a field”, J. Math. Sci. (New York), 95:2 (1999), 2096–2101        
35. V. I. Mysovskikh, “On the lattice of subgroups normalized by a symmetric one in the complete monomial group”, J. Math. Sci. (New York), 95:2 (1999), 2111–2115        
36. A. A. Panin, A. V. Yakovlev, “The Galois theory for a class of modular lattices”, J. Math. Sci. (New York), 95:2 (1999), 2126–2135        
37. Alan Harebov, Nikolai Vavilov, “On the lattice of subgroups of chevalley groups containing a split maximal torus”, Communications in Algebra, 24:1 (1996), 109  
38. N. A. Vavilov, “Linear groups generated by one-parameter groups of one-dimensional transformations”, Russian Math. Surveys, 44:1 (1989), 265–266            
39. N. A. Vavilov, “Subgroups of split orthogonal groups over a ring”, Siberian Math. J., 29:4 (1988), 537–547        
40. N. A. Vavilov, “Subgroups of split orthogonal groups”, Siberian Math. J., 29:3 (1988), 341–352        
41. Z. I. Borevich, N. A. Vavilov, “Definition of a net subgroup”, J Math Sci, 30:1 (1985), 1810  
42. N. A. Vavilov, E. V. Dybkova, “Subgroups of the full symplectic group containing the group of diagonal matrices. II”, J Math Sci, 30:1 (1985), 1823  
43. L. Yu. Kolotilina, “Aplication of net subgroups to the theory of sparse matrices”, J Math Sci, 29:6 (1985), 1714  
44. N. A. Vavilov, “On subgroups of the unitary group over a semilocal ring”, Russian Math. Surveys, 37:4 (1982), 145–146            
45. N. A. Vavilov, “A Bruhat decomposition for subgroups containing the group of diagonal matrices. II”, J. Soviet Math., 27:4 (1984), 2865–2874      
46. Kh. Roloff, “Lower central series and derived series of net subgroups of the general linear group”, J. Soviet Math., 27:4 (1984), 2968–2974      
47. N. A. Vavilov, E. B. Plotkin, “Net subgroups of Chevalley groups. II. Gauss decomposition”, J. Soviet Math., 27:4 (1984), 2874–2885      
48. A. E. Zalesskii, “Linear groups”, Russian Math. Surveys, 36:5 (1981), 63–128            
49. I. D. Suprunenko, “Subgroups of $G(n,p)$ containing $SL(2,p)$ in an irreducible representation of degree $n$”, Math. USSR-Sb., 37:3 (1980), 425–440          
50. E. V. Dybkova, “The index of a net subgroup of a symplectic group over a Dedekind ring”, J. Soviet Math., 37:2 (1987), 964–974      
51. Z. I. Borevich, “Subgroups of linear groups rich in transvections”, J. Soviet Math., 37:2 (1987), 928–934      
52. Z. I. Borevich, N. A. Vavilov, “Subgroups of the full linear group over a semilocal ring”, J. Soviet Math., 37:2 (1987), 935–937      
53. N. A. Vavilov, “Parabolic subgroups of Chevalley groups over a semilocal ring”, J. Soviet Math., 37:2 (1987), 942–952