01.01.06 (Mathematical logic, algebra, and number theory)
group cohomology; diagram geometries; sporadic groups; integral lattices.
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.
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.
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.