Normality of elementary subgroup in $\operatorname{Sp}(2,A)$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 33-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $A$ be a ring with involution (associative, with identity), $e_1,\dots,e_n$ be a full system of hermitian idempotents in $A$ such that every $e_i$ generates $A$ as a two-sided ideal. This paper proves normality of the elementary subgroup in $\operatorname{Sp}(2,A)$ if $n\ge3$ and $A$ satisfies an analog of local stable rank condition.
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E. Yu. Voronetsky. Normality of elementary subgroup in $\operatorname{Sp}(2,A)$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 33-45. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a3/

[1] N. A. Vavilov, V. A. Petrov, “O nadgruppakh $\mathrm{Ep}(2l, R)$”, Algebra i analiz, 15:4 (2003), 72–114 | MR | Zbl

[2] N. A. Vavilov, A. V. Stepanov, “Nadgruppy poluprostykh grupp”, Vestnik SamGU, 3 (2008), 51–95 | MR | Zbl

[3] V. I. Kopeiko, “Stabilizatsiya simplekticheskikh grupp nad koltsom mnogochlenov”, Matem. sb., 106(148):1(5) (1978), 94–107 | MR | Zbl

[4] V. A. Petrov, A. K. Stavrova, “Elementarnye podgruppy v izotropnykh reduktivnykh gruppakh”, Algebra i analiz, 20:4 (2008), 160–188 | MR | Zbl

[5] A. A. Suslin, V. I. Kopeiko, “Kvadratichnye moduli i ortogonalnye gruppy nad koltsami mnogochlenov”, Zap. nauchn. semin. LOMI, 71, 1977, 216–250 | MR | Zbl

[6] A. Bak, N. Vavilov, “Structure of Hyperbolic Unitary Groups. I : Elementary Subgroups”, Algebra Colloq., 7:2 (2000), 159–196 | DOI | MR | Zbl

[7] D. Costa, G. Keller, “Radix Redux: normal subgroups of symplectic groups”, J. reine angew. Math., 427 (1992), 51–105 | MR | Zbl

[8] R. Hazrat, N. Vavilov, “Bak's work on the $ K$-theory of rings”, J. K-Theory, 4 (2009), 1–65 | DOI | MR | Zbl

[9] R. Hazrat, N. Vavilov, “$ K_1$ of Chevalley groups are nilpotent”, J. Pure Appl. Algebra, 179 (2003), 99–116 | DOI | MR | Zbl

[10] A. Lavrenov, “Another presentation for symplectic Steinberg groups”, J. Pure Appl. Algebra, 219:9 (2015), 3755–3780 | DOI | MR | Zbl

[11] V. A. Petrov, “Overgroups of Unitary Groups”, K-Theory, 29 (2003), 147–174 | DOI | MR | Zbl

[12] A. Stepanov, N. Vavilov, “Decomposition of transvections: a theme with variations”, K-Theory, 19 (2000), 109–153 | DOI | MR | Zbl

[13] A. A. Suslin, “Algebraic $K$-theory”, J. Sov. Math., 28:6 (1985), 870–923 | DOI | MR | Zbl

[14] G. Taddei, “Invariance du sous-groupe symplectique élémentaire dans le groupe symplectique sur un anneau”, C. R. Acad. Sci Paris, Sér. I, 295:2 (1982), 47–50 | MR | Zbl

[15] G. Taddei, “Normalité des groupes élémentaire dans les groupes de Chevalley sur un anneau”, Applications of algebraic K-theory to algebraic geometry and number theory, Part II, Contemp. Math., 55, 1986, 693–710 | DOI | MR | Zbl

[16] L. N. Vaserstein, H. You, “Normal subgroups of classical groups over rings”, J. Pure Appl. Algebra, 105:1 (1995), 93–106 | DOI | MR