3.3. The greatest common divisor and the least common multiple 12 3.4. Parabolic divisors 14 3.5. Divisibility: further properties 14 4. Normal forms arising from HNN extensions 16 4.1. HNN -normal form 16 5. Conjugacy problem 18 5.1. Conjugacy Criterion for HNN -extensions 18 5.2. Block decomposition 22 5.3. Conjugacy with respect to a subgroup 23 5.4. An algorithm for solving the Conjugacy Pr...

1 An algebra H(Gm) of double-cosets is constructed for every finite Weilrepresentation Gm. For the Clifford-Weil groups Gm = Cm(ρ) associated to some classical Type ρ of self-dual codes over a finite field, this algebra is shown to be commutative. Then the eigenspace-decomposition ofH(Cm(ρ)) acting on the space of degree N invariants of Cm(ρ) may be obtained from the kernels of powers of the co...

Let CAn=C[S2?S2???S2] be the group algebra of an n-step iterated wreath product. We prove some structural properties An such as their centers, centralizers, and right double cosets. apply these results to explicitly write down Mackey theorem for groups give a partial description natural transformations between induction restriction functors on representations product tower by computing certain ...

This is the author's second paper treating double coset problem for classical groups. Let G be an algebraic group over algebraically closed field K . The consists of classifying pairs H , J connected subgroups with finitely many ( ) -double cosets in critical setup occurs when reductive and a parabolic subgroup. Assume that group, simple maximal P k stabilizer totally singular -space. We show i...

The concept of an n-dimensional local field was introduced by A.N. Parshin [Pa1] with the aim of generalizing the classical adelic formalism to (absolutely) ndimensional schemes. By definition, a 0-dimensional local field is just a finite field, and an n-dimensional local field, n > 0, is a complete discrete valued field whose residue field is (n − 1)-dimensional local. Thus for n = 1 we get lo...

Consider an infinite homogeneous tree $T_n$ of valence $n+1$, its group $Aut(T_n)$ automorphisms, and the $Hie(T_n)$ spheromorphisms (hierarchomorphisms), i.~e., homeomorphisms boundary that locally coincide with transformations defined by automorphisms. We show subgroup is spherical in $Hie(T_n)$, any irreducible unitary representation contains at most one $Aut(T_n)$-fixed vector. present a co...

We enlarge a Coxeter group into category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This singular monoid, is connected to geometry partial flag varieties. Our main result presentation this category by generators and relations. also provide new description reduced expressions describe all braid relations between such expressions, prove an an...

We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, long Dehn filling of one cusp in this admits This is constructed several stages, using results about separability peripheral subgroups and their double cosets, addition to new conjugacy theorem may be independent interest. The infinite sequence triangulation...

Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...