Hamann, Kaylee Joy

In the field of several complex variables, one of the most important questions that remains to be answered is the voracity of the Greene-Krantz conjecture:Conjecture 0.0.1. Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(x)} accumulates at a boundary point p ∈ ∂D for some x∈D. Then ∂D is of finite type at ...

Zhuchok, A. V.
Published in
Siberian Mathematical Journal

A. P. Pozhidaev proved that each dialgebra may be embedded into a dialgebra with a barunit. As is known, a dialgebra is a vector space with two binary operations satisfying the axioms of a dimonoid. It is natural in this situation to pose the problem about the possibility of adjoining bar-units to dimonoids in a given class and the problem of embed...

Azarov, D. N.
Published in
Russian Mathematics

Let a group Gsatisfy condition A: for every positive integer n the number of all subgroups of the group G of index n is finite. We prove that if G is virtually residually finite p-group for some prime p, then the automorphism group of the group G is virtually residually finite p-group. A similar result is obtained for a split extension of the group...

Osipov, D. V.
Published in
Mathematical Notes

Trofimov, V. I.
Published in
Proceedings of the Steklov Institute of Mathematics

It is proved that results from a previous paper of the author on symmetrical 2-extensions of graphs can be extended to symmetrical p-extensions of graphs for any prime p. In particular, it is proved that, for any prime p, there are only finitely many symmetrical p-extensions of a locally finite graph with an abelian subgroup of finite index in its ...

Lin, Vladimir Zaidenberg, Mikhail

The configuration space $\mathcal{C}^n(X)$of an algebraic curve $X$ is the algebraic variety consisting ofall $n$-point subsets $Q\subset X$. We describe theautomorphisms of $\mathcal{C}^n(\mathbb{C})$, deduce that the(infinite dimensional) group $\Aut\mathcal{C}^n(\mathbb{C})$ issolvable, and obtain an analog of the Mostow decomposition in thisgro...

Thas, Koen

We describe new classification results in the theory of generalized quadrangles (= Tits-buildings of rank 2 and type B2), more precisely in the (large) subtheory of skew translation generalized quadrangles (``STGQs''). Some of these involve, and solve, long-standing open problems.

Ahlman, Ove Koponen, Vera

A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of c...

Thas, Koen

We describe new classification results in the theory of generalized quadrangles (= Tits-buildings of rank 2 and type B-2), more precisely in the (large) subtheory of skew translation generalized quadrangles ("STGQs"). Some of these involve, and solve, long-standing open problems.

Timoshenko, E. I.
Published in
Mathematical Notes

Automorphisms of a partially commutative metabelian group SΓ defined by a finite simple graph Γ with r vertices are considered. The monoid P of matrices of order r is equipped with a congruence ≈. It is proved that the group of automorphisms acting identically on the quotient group by the commutator subgroup SΓ/[SΓ,SΓ] is isomorphic to the quotient...