We prove that whenever a Kac-Moody group over a finite field is a lattice of its buildings, it has a fundamental domain with respect to which the induction cocycle is L for any p∈ [1; +∞). The proof uses elementary counting arguments for root group actions on buildings. The applications are the possibility to apply some lattice superrigidity, and the normal subgroup property for Kac-Moody latti...

One way to view Theorem 1.1 is as a statement that the algebraic structure of a finitely generated profinite group somehow also encodes the topological structure. That is, if one wishes to know the open subgroups of a profinite group G, a topological property, one must only consider the subgroups of G of finite index, an algebraic property. As profinite groups are compact topological spaces, an...

We show that the normal closure of any periodic element mapping class group a nonorientable surface whose order is greater than 2 contains commutator subgroup, which for g≥7 equal to twist and provide necessary sufficient conditions closures involutions contain subgroup. Finally, we criterion normally generate M(Ng) give examples.

Let Jl consist of the groups GÍL m) = (a, b; a~ b a = b"1) where |/.| 4 1 4 |zzi|, lm40 and l, m are coprime. We characterize the endomorphisms of these groups, compute the centralizers of special elements and show that the endomorphism a —• a, b —' b is onto with a nontrivial fully invariant kernel. Hence G(l, m) is non-Hopfian in the'fully invariant sense.' Our purpose is to prove the results...

The gammaA2-subgroup of gammaA-globulins, previously delineated by antigenic studies, was found to differ strikingly from other immunoglobulins in the manner in which the polypeptide chains are bound together. The heavy and light chains were not linked to each other by disulfide bonds. Instead the light chains were disulfide linked to one another, and were present in the gammaA2-molecule as dis...

a subgroup h of a group g is called inert if‎, ‎for each $gin g$‎, ‎the index of $hcap h^g$ in $h$ is finite‎. ‎we give a classification ‎of soluble-by-finite groups $g$ in which subnormal subgroups are inert in the cases where $g$ has no nontrivial torsion normal subgroups or $g$‎ ‎is finitely generated‎.

In this paper, we have focused to study convex L-subgroups of an Lordered group. First, we introduce the concept of a convex L-subgroup and a convex L-lattice subgroup of an L-ordered group and give some examples. Then we find some properties and use them to construct convex L-subgroup generated by a subset S of an L-ordered group G . Also, we generalize a well known result about the set of all...

Let G G be a non-compact connected semisimple real Lie group with finite center. Suppose L"> L encoding="application/x...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

In the study of the relation between the mapping class group ? g of a surface g of genus g and the theory of nite-type invariants of homology 3-spheres, three subgroups of ? g play a large role. They are the Torelli group T g , the Johnson subgroup K g and a new subgroup L L g , which contains K g , deened by a choice of a Lagrangian subgroup L H 1 ((g). In this work we determine the quotient L...