Russian version
Scientific publications
Preprints and manuscripts
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A.Stepanov. Structure theory and subgroups of Chevalley groups over rings.
Doctor of Science Thesis. 2014. Russian full text.
Abstract (in Russian).
Published and accepted articles
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A.Stavrova, A.Stepanov,
Normal structure of isotropic reductive groups over rings.
J. Algebra (2022), https://doi.org/10.1016/j.jalgebra.2022.11.014.
Preprint:
arXiv 1801.08748.
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Ya.Nuzhin, A.Stepanov,
Bruhat Decomposition for Carpet Subgroups of Chevalley Groups Over Fields.
Algebra and Logic 60:5 (2021), 327-335. DOI 10.1007/s10469-021-09658-4.
Preprint (Russian).
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R.A.Lubkov, A.V.Stepanov
Subgroups of Chevalley groups over rings. Journal of Mathematical Sciences (New York).
252:6 (2021), 829–840
Full text.
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Ya.Nuzhin, A.Stepanov,
Subgroups of Chevalley groups of types Bl and Cl
contaning the groups over a subring and corresponding carpets.
St.Petersburg Math. J. 31:4 (2020), 719–737.
arXiv preprint (in Russian)
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A.Bak, A.Stepanov,
Subring subgroups in symplectic group in characteristic 2. St.Petersburg Math. J.
28:4 (2017), 465–475.
Link to arXiv
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A.Stepanov, A new look at the decomposition of unipotents and the normal structure of
Chevalley groups. St.Petersburg Math. J. 28:3 (2017), 411-419.
Link to arXiv.
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W.Holubowski, A.Stepanov,
Bijections preserving commutators and automorphisms of unitriangular group.
Linear and Multilinear Algebra 65:1 (2017), 23–34.
DOI:10.1080/03081087.2016.1165170.
Preprint arXiv version
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A.Stepanov,
Structure of Chevalley groups over rings via universal localization.
J. Algebra 450 (2016), 522–548. DOI:10.1016/j.jalgebra.2015.11.031.
Link to arXiv.
(the title of the first version was "Universal localization in algebraic groups").
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A.V.Stepanov,
Sandwich classification theorem. Int. J. Group Theory 4:3 (2015), 7–12.
Link to the article.
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A.Stepanov, Nonabelian K-theory for Chevalley groups over rings.
J. Math. Sci. (New York) 209:4 (2015), 645–656.
English preprint
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H.Apte, A.Stepanov,
Local-global principle for congruence subgroups of Chevalley groups.
Central European J. Math. 12:6 (2014), 801–812.
DOI: 10.2478/s11533-013-0391-9.
Full text
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R. Hazrat, A. Stepanov, N. Vavilov, Zhang Zuhong.
The yoga of commutators: Further applications,
J. Math. Sci. (New York) 200:6 (2014), 742–768.
(reprinted from Zapiski nauchnyh seminarov POMI 421 (2014), 166–213)
Full text
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A.Stepanov,
Elementary calculus in Chevalley groups over rings.
J. Prime Research in Math. 9 (2013), 79–95.
Full text
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R.Hazrat, A.Stepanov, N.Vavilov, Z.Zhang,
Commutator width in Chevalley groups.
Note di Matematica 33:1 (2013), 139–170
Link to ArXiv
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A.V.Stepanov,
Subring subgroups in Chevalley groups with doubly laced root systems.
J.Algebra 362 (2012), 12–29.
Full text
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N.A.Vavilov, A.V.Stepanov,
Linear groups over general rings. I. Generalities.
J. Math. Sci. (New York) 188:5 (2013), 490–550
Full text
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R. Hazrat, A. Stepanov, N. Vavilov, Zhang Zuhong. The yoga of commutators,
J. Math. Sci. (New York) 179:6 (2011), 662–678
Full text
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A.V.Stepanov, N.A.Vavilov,
Length of commutators in Chevalley groups.
Israel J. Math. 185 (2011), 253–276.
Full text
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A.V.Stepanov,
Free product subgroups between Chevalley groups
G(Φ,F) and G(Φ,F[t]),
J.Algebra 324 (2010), 1549–1557.
Full text
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N.A.Vavilov and A.V.Stepanov, Standard commutator formulae, revisited.
Vestnik St.Petersburg Univ., Math., 43 (2010), no.1, 12–17
Full text
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A.Luzgarev, A.Stepanov, N.Vavilov, Calculations in exceptional groups over rings,
Reprint: J. Math. Sci. (New York) 168:3 (2010), 334–348
Full text
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V.V.Nesterov, A.V.Stepanov,
The identity with constants in a Chevalley group of type F4.
St.Petersburg Math. J., 21:5 (2010), 819–823
Full text
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N.A.Vavilov, A.V.Stepanov,
Overgroups of semisimple groups.
Vestnik Samarskogo gos. un-ta. Estestvennonauchnaya ser.,
N.3(62) (2008), 51–95 (in Russian)
Full text
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N.A.Vavilov and A.V.Stepanov, Standard commutator formulae.
Vestnik St.Petersburg Univ., Math., (2008), No.1, 5–8
Full text
I apologize for the quality of translation,
it was done by a "professional" translator.
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A.V.Stepanov,
Nonstandard subgroups between En(R) and
GLn(A).
Algebra Colloquium 10:3 (2004), 321–334
Full text
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A.V.Stepanov,
Several constructions of exact sequences. J. Math. Sci. (New York)
116:1 (2003), 3052–3062
Full text
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A.Bak, A.V.Stepanov,
Dimension theory and nonstable K-theory for net groups.
Rendiconti del Seminario Matematico dell'Universitá di
Padova, 106 (2001), 207–253
Full text. A simple
group theoretical lemma
to clarify the proof of Dennis–Vaserstein decomposition (Theorem 4.6).
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A.V.Stepanov, N.A.Vavilov,
Decomposition of transvections: Theme with variations.
K-Theory 19:2 (2000), 109–153.
Full text
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A.S.Sivatski, A.V.Stepanov,
On the word length of commutators in GLn(R). K-Theory
17:4 (1999), 295–302
Full text
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A.V.Stepanov,
On the normal structure of the general linear group over a ring.
J. Math. Sci. (New York) 95:2 (1999),
2146–2155
Full text
There is a misprint and an error in Proposition 1.9.
Corrections.
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A.V.Stepanov,
On the distribution of subgroups normalized by a fixed subgroup.
J. Soviet Math. 64 (1993), 769–776
Full Text
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N.A.Vavilov, E.B.Plotkin, A.V.Stepanov,
Calculations in Chevalley groups over commutative rings.
Soviet Math. Doklady 40:1 (1990), 145–147.
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N.A.Vavilov, A.V.Stepanov,
Subgroups of the general linear group over a ring that satisfies stability
conditions. Sov. Math. (Izv. VUZ) 33:10 (1989),
23–31.
Russian text
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A.V.Stepanov,
Stable rank and stability of arbitrary rows. Russian Math. Surveys
44:2 (1989), 295–296.
Russian text
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A.V.Stepanov,
Description of subgroups of the general linear group over a ring with
the use of stability conditions. In: Rings and linear
groups. Kubansky State University (1988), Krasnodar. 82–91 (Russian).
Russian text
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A.V.Stepanov,
A ring of finite stable rank is not necessarily finite in the sense of
Dedekind. Soviet Math. Doklady 36:2 (1988),
301–304.Full text (not very good scan)
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A.V.Stepanov,
Ideal stable rank of rings. Vestnik Leningrad. Univ., Math.,
no. 3 (1986), 61–68.
All full text articles presented on this page are preprint versions preparated by the authors.
Russian originals of some papers can be downloaded from here.
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