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Burichenko Vladimir Petrovich

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Total publications: 10
Scientific articles: 10

Number of views:
This page:593
Abstract pages:1526
Full texts:385
References:214
Candidate of physico-mathematical sciences (1993)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 07.05.1966
E-mail: ,
Keywords: group cohomology; diagram geometries; sporadic groups; integral lattices.

Subject:

I am interested in 1) non-splitting extensions of simple groups, and the related low-dimensional cohomology groups, and 2) diagram geometries, their cohomology properties and applications to the computation of cohomology of the groups acting on these geometries. Main results are: 1) calculation of the relations module of arbitrary Coxeter group; 2) classification of all non-splitting extensions of an elementary abelian 2-group $V$ by means of $L_2(q)$ such that $L_2(q)$ acts on $V$ nontrivially and irreducibly; 3) a theorem on extension of cocycles in BN-pairs. Let $M$ be a module over a BN-pair $G$, $B$ a fixed Borel subgroup. Suppose we have an $M$-valued $k$-cocycle on each parabolics of rank $k+1$ containing $B$, and suppose these cocycles coincide on intersections. Then these cocycles are restriction of a cocycle defined on the whole group $G$. The similar statement is true for the groups admitting a flag-transitive action on a dimensional linear space; 4) calculation of the homology of the flag complexes of the rank 4 geometry, related to the Higman–Sims group, and of the locally polar spaces of order 2.

Biography

Graduated from Moscow University in 1988. In 1988–91 a postgraduate student in the V. A. Steklov Institute of mathematics. Received Ph.D. in 1993, under supervision of Prof. A. I. Kostrikin. Title of Ph.D.Thesis: "Lattices, related to exceptional Lie algebras". Since 1992 a researcher in the Institute of mathematics of the Belarus National Academy of Sciences. My list of publications contains 12 articles.

   
Main publications:
  • V. P. Burichenko. On homological properties of the rank 4 geometry related to the Higmanndash;Sims group // Communs. in Algebra, 2001, 29 (9), 3989–4010.
  • V. P. Burichenko. Extensions of cocycles in BN-pairs // J.Algebra, 1998, 210 (1), 1–30.
  • V. P. Burichenko. On homological property of groups acting on linear spaces // J. Math. Sci (New York), 2000, 100 (1), 2003–2012.
  • V. P. Burichenko. On extensions of Coxeter groups // Communs. in Algebra, 1995, 23 (5), 1867–1897.

http://www.mathnet.ru/eng/person18024
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/266561

Publications in Math-Net.Ru
2014
1. V. P. Burichenko, “Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups”, Mat. Tr., 17:1 (2014),  19–69  mathnet  mathscinet; Siberian Adv. Math., 25:2 (2015), 77–109
2013
2. V. P. Burichenko, “On the space $\operatorname{Ext}$ for the group $SL(2,q)$”, Mat. Tr., 16:1 (2013),  28–55  mathnet  mathscinet  elib; Siberian Adv. Math., 24:2 (2014), 100–118
3. V. P. Burichenko, “Some finiteness questions about formations”, Tr. Inst. Mat., 21:1 (2013),  15–24  mathnet
2012
4. V. P. Burichenko, “On Groups Whose Small-Order Elements Generate a Small Subgroup”, Mat. Zametki, 92:3 (2012),  361–367  mathnet  mathscinet  zmath  elib; Math. Notes, 92:3 (2012), 327–332  isi  elib  scopus
2008
5. V. P. Burichenko, “2-Cohomologies of the groups $SL(n,q)$”, Algebra Logika, 47:6 (2008),  687–704  mathnet  mathscinet  zmath  elib; Algebra and Logic, 47:6 (2008), 384–394  isi  scopus
6. V. P. Burichenko, “Formations generated by a group of socle length 2”, Sibirsk. Mat. Zh., 49:6 (2008),  1238–1249  mathnet  mathscinet; Siberian Math. J., 49:6 (2008), 988–996  isi  scopus
2007
7. V. P. Burichenko, “The 2-cohomology of the group $\Omega^-(4,q)$ with coefficients in the natural module”, Mat. Sb., 198:9 (2007),  29–42  mathnet  mathscinet  zmath  elib; Sb. Math., 198:9 (2007), 1247–1260  isi  scopus
2000
8. V. P. Burichenko, “Extensions of abelian 2-groups by means of $L_2(q)$ with irreducible action”, Algebra Logika, 39:3 (2000),  280–319  mathnet  mathscinet  zmath; Algebra and Logic, 39:3 (2000), 160–183  scopus
1993
9. V. P. Burichenko, “Invariant lattices in the Steinberg module and their isometry groups”, Mat. Sb., 184:12 (1993),  145–156  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 80:2 (1995), 519–529  isi
1991
10. V. P. Burichenko, “On a special loop, the discon form, and the lattice connected with $O_7(3)$”, Mat. Sb., 182:10 (1991),  1408–1429  mathnet  mathscinet  zmath; Math. USSR-Sb., 74:1 (1993), 145–167  isi

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