相关论文: On the subgroup structure of the hyperoctahedral g…

We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.

Hyperoctahedral homology is the homology theory associated to the hyperoctahedral crossed simplicial group. It is defined for involutive algebras over a commutative ring using functor homology and the hyperoctahedral bar construction of…

We extend the Schur algebra and the polynomial web category of the symmetric group to the hyperoctahedral group. In particular, we define the hyperoctahedral web category diagrammatically by generators and relations, and prove that it is…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the…

We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…

There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…

We compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the…

We explicitly compute the lower algebraic K-theory of the split three-dimensional crystallographic groups; i.e., the groups G that act properly and cocompactly on three-dimensional Euclidean space by isometries, such that the natural map…

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts. In this article we tie recent work on various other natural overgroups, in…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the…

Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…

We compute and analyze isotropy subgroups of the complex orthogonal group with respect to the similarity transformation on itself and on skew-symmetric matrices. Their group structure is related to a group of certain nonsingular block…

Similar to the symplectic cases, there is a family of fourteen orthogonal hypergeometric groups with a maximally unipotent monodromy (cf. Table 1.1). We show that two of the fourteen orthogonal hypergeometric groups associated to the pairs…

We provide a procedure for generating the irreducible representations of crystallography groups in any dimension. We also furnish a strategy to investigate the topology of the unitary dual of a crystallography group using sequences of…

We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…