## Scientific publications## Preprints and manuscripts- A.Stepanov. Structure theory and subgroups of Chevalley groups over rings. Doctor of Science Thesis. 2014. Russian full text. Abstract (in Russian).
## Published articles-
A.Bak, A.Stepanov,
Subring subgroups in symplectic group in characteristic 2.
*St.Petersburg Math. J.***28**:4 (2017), 465–475. Link to arXiv -
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. -
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 -
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"). -
A.V.Stepanov,
Sandwich classification theorem.
*Int. J. Group Theory***4**:3 (2015), 7–12. Link to the article. -
A.Stepanov, Nonabelian K-theory for Chevalley groups over rings.
*J. Math. Sci. (New York)***209**:4 (2015), 645–656. English preprint -
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 -
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 -
A.Stepanov,
Elementary calculus in Chevalley groups over rings.
*J. Prime Research in Math.***9**(2013), 79–95. Full text -
R.Hazrat, A.Stepanov, N.Vavilov, Z.Zhang,
Commutator width in Chevalley groups.
*Note di Matematica***33**:1 (2013), 139–170 Link to ArXiv -
A.V.Stepanov,
Subring subgroups in Chevalley groups with doubly laced root systems.
*J.Algebra***362**(2012), 12–29. Full text -
N.A.Vavilov, A.V.Stepanov,
Linear groups over general rings. I. Main structure theorems.
*J. Math. Sci. (New York)***188**:5 (2013), 490–550 Russian text -
R. Hazrat, A. Stepanov, N. Vavilov, Zhang Zuhong. The yoga of commutators,
*J. Math. Sci. (New York)***179**:6 (2011), 662–678 Full text -
A.V.Stepanov, N.A.Vavilov,
Length of commutators in Chevalley groups.
*Israel J. Math.***185**(2011), 253–276. Full text -
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 -
N.A.Vavilov and A.V.Stepanov, Standard commutator formulae, revisited.
*Vestnik St.Petersburg Univ., Math.*,**43**(2010), no.1, 12–17 Full text -
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 -
V.V.Nesterov, A.V.Stepanov,
The identity with constants in a Chevalley group of type F
_{4}.*St.Petersburg Math. J.*,**21**:5 (2010), 819–823 Full text -
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 -
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. -
A.V.Stepanov,
Nonstandard subgroups between E
and GL_{n}(R)._{n}(A)*Algebra Colloquium***10**:3 (2004), 321–334 Full text -
A.V.Stepanov,
Several constructions of exact sequences.
*J. Math. Sci. (New York)***116**:1 (2003), 3052–3062 Full text -
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). -
A.V.Stepanov, N.A.Vavilov,
Decomposition of transvections: Theme with variations.
*K-Theory***19**:2 (2000), 109–153. Full text -
A.S.Sivatski, A.V.Stepanov,
On the word length of commutators in GL
_{n}(R).*K-Theory***17**:4 (1999), 295–302 Full text -
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. -
A.V.Stepanov,
On the distribution of subgroups normalized by a fixed subgroup.
*J. Soviet Math.***64**(1993), 769–776 Full Text -
N.A.Vavilov, E.B.Plotkin, A.V.Stepanov,
Calculations in Chevalley groups over commutative rings.
*Soviet Math. Doklady***40**:1 (1990), 145–147. -
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 -
A.V.Stepanov,
Stable rank and stability of arbitrary rows.
*Russian Math. Surveys***44**:2 (1989), 295–296. Original Russian text -
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 -
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) -
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. |