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.
V. P. Burichenko, “On bilinear complexity of multiplcation of a $3\times 2$ matrix by a $2\times 3$ matrix”, Diskr. Mat., 36:1 (2024), 15–45
2023
2.
V. P. Burichenko, “Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II”, Tr. Inst. Mat., 31:1 (2023), 101–111
2022
3.
V. P. Burichenko, “Non-existence of a short algorithm for multiplication of $3\times3$ matrices with group $S_4\times S_3$”, Tr. Inst. Mat., 30:1-2 (2022), 99–116
2016
4.
V. P. Burichenko, “The isotropy group of the matrix multiplication tensor”, Tr. Inst. Mat., 24:2 (2016), 106–118
2014
5.
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; Siberian Adv. Math., 25:2 (2015), 77–109
V. P. Burichenko, “Some finiteness questions about formations”, Tr. Inst. Mat., 21:1 (2013), 15–24
2012
8.
V. P. Burichenko, “On Groups Whose Small-Order Elements Generate a Small Subgroup”, Mat. Zametki, 92:3 (2012), 361–367; Math. Notes, 92:3 (2012), 327–332
V. P. Burichenko, “Formations generated by a group of socle length 2”, Sibirsk. Mat. Zh., 49:6 (2008), 1238–1249; Siberian Math. J., 49:6 (2008), 988–996
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; Sb. Math., 198:9 (2007), 1247–1260
V. P. Burichenko, “Extensions of abelian 2-groups by means of $L_2(q)$ with irreducible action”, Algebra Logika, 39:3 (2000), 280–319; Algebra and Logic, 39:3 (2000), 160–183
V. P. Burichenko, “Invariant lattices in the Steinberg module and their isometry groups”, Mat. Sb., 184:12 (1993), 145–156; Russian Acad. Sci. Sb. Math., 80:2 (1995), 519–529
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; Math. USSR-Sb., 74:1 (1993), 145–167
V. P. Burichenko, “Transitive orthogonal decompositions of simple complex Lie algebras of type $F_4$ and $E_6$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, no. 4, 78–80
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