Homology of tangent groups considered as discrete groups and scissors congruence

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

Homology Isomorphisms between Algebraic Groups Made Discrete

THEOREM 1. Consider a split exact sequence of discrete groups Suppose there exists a normal series G = G 0 > G , o ... >(? " ^G n+1 = {1} (• •) such that: (1) GJG i+1 is a rational vector space for i = 0, ...,«; (2) GJG i+1 is contained in the centre ofG/G i+1 for i = 0,...,n; (3) there exists an element in the centre of T/G that induces a diagonalizable endomorphism of each GJG i+1 with all ei...

Structural Properties of Inner Amenable Discrete Groups

Volumes of Discrete Groups and Topological Complexity of Homology Spheres

Can one ascribe a “size” to a discrete group? By that we mean a real-valued invariant, μ(Γ) satisfying the following condition: for any subgroup ∆ < Γ of finite index, μ(∆) = (Γ : ∆)μ(Γ). The importance of such an invariant for the structure of Γ is clear from the following observation: if μ(Γ) > 0 and ∆1,∆2 are two isomorphic subgroups of Γ of finite index, then (Γ : ∆1) = (Γ : ∆2). Some ratio...

Topological K-(co-)homology of Classifying Spaces of Discrete Groups

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction EG×G X of a proper G-CW -complex X satisfying certain finiteness conditions. In particular we give formulas computing the topological K-(co)homology K∗(BG) and K(BG) up to finite abelian torsion groups. They apply for instance to arithmetic groups, word hyperbolic gr...