Geodesic
Overgroups of the diagonal group in the hyperbolic unitary group over a simple Artin ring. II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 17, Tome 356 (2008), pp. 85-117 
E. V. Dybkova. Overgroups of the diagonal group in the hyperbolic unitary group over a simple Artin ring. II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 17, Tome 356 (2008), pp. 85-117. http://geodesic.mathdoc.fr/item/ZNSL_2008_356_a2/
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     title = {Overgroups of the diagonal group in the hyperbolic unitary group over a~simple {Artin} {ring.~II}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We continue our previous paper, where we have described the lattice of overgroups of the diagonal subgroup in the hyperbolic unitary group for a infinite or enough large simple Artin ring. Here we consider the same problem for the hyperbolic unitary group of the second degree over a finite simple Artin ring with a small center. We state the conditions, under which the above lattice admits the standard description. Bibl. – 11 titles.

[1] E. V. Dybkova, “Naddiagonalnye podgruppy giperbolicheskoi unitarnoi gruppy dlya khoroshego formennogo koltsa nad polem”, Zap. nauchn. semin. POMI, 236, POMI, SPb., 1997, 87–96 | MR | Zbl

[2] E. V. Dybkova, “Formennye seti i reshetka naddiagonalnykh podgrupp simplekticheskoi gruppy nad polem kharakteristiki 2”, Algebra i analiz, 10:4 (1998), 113–129 | MR | Zbl

[3] E. V. Dybkova, “Naddiagonalnye podgruppy giperbolicheskoi unitarnoi gruppy dlya khoroshego formennogo koltsa nad nekommutativnym telom”, Zap. nauchn. semin. POMI, 305, POMI, SPb., 2003, 121–135 | MR

[4] E. V. Dybkova, “Teorema Borevicha dlya giperbolicheskoi unitarnoi gruppy nad nekommutativnym telom”, Zap. nauchn. semin. POMI, 321, POMI, SPb., 2005, 136–167 | MR | Zbl

[5] E. V. Dybkova, “Nadgruppy diagonalnoi gruppy v giperbolicheskoi unitarnoi gruppe nad prostym artinovym koltsom. I”, Zap. nauchn. semin. POMI, 338, POMI, SPb., 2006, 155–172 | MR | Zbl

[6] Zh. Dedonne, Geometriya klassicheskikh grupp, Mir, M., 1974 | MR

[7] A. Bak, “On modules with quadratic forms”, Algebraic $K$-Theory and its Geometric Applications, Lect. Notes Math., 108, Springer, Berlin, 1969, 55–66 | MR

[8] A. Bak, $K$-theory of forms, Ann. Math. Stud., 98, Princeton Univ. Press, Princeton, NY, 1981 | MR | Zbl

[9] A. Bak, N. Vavilov, “Structure of hyperbolic unitary groups. I. Elementary subgroups”, Algebra Colloq., 7:2 (2000), 159–196 | DOI | MR | Zbl

[10] A. J. Hahn, O. T. O'Meara, The classical groups and $K$-theory, Springer, Berlin, 1989 | MR | Zbl

[11] O. King, “Subgroups of the special linear group containing the diagonal subgroup”, J. Algebra, 132 (1990), 198–204 | DOI | MR | Zbl