We study the question of surjectivity Galois correspondence from subHopf algebras to subfields given by Fundamental Theorem Theory for abelian Hopf structures on a extension fields with group G', finite p-group. Applying connection between regular subgroups holomorph p-group (G, +) and associative, commutative nilpotent algebra A Caranti, et. al., we show that if gives rise H-Hopf structure L/K...

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. Moreover, the 2-regular case is precisely the class of totally real number fields that have homotopy cartesian “Bökstedt square”, relating the K-theory of the 2-integers to that of the fields of real and co...

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. W...

The sandpile group of a graph G is an abelian group whose order is the number of spanning trees of G. We find the decomposition of the sandpile group into cyclic subgroups when G is a regular tree with the leaves are collapsed to a single vertex. This result can be used to understand the behavior of the rotor-router model, a deterministic analogue of random walk studied first by physicists and ...

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

The sandpile group of a connected graph is the group of recurrent configurations in the abelian sandpile model on this graph. We study the structure of this group for the case of regular trees. A description of this group is the following: Let T (d, h) be the d-regular tree of depth h and let V be the set of its vertices. Denote the adjacency matrix of T (d, h) by A and consider the modified La...