Some extreme discrete groups

Some Finite and Discrete Groups

We have have encountered several finite groups in the previous chapter: the cyclic group Zn, the symmetric group Sn, and its subgroup the alternating group An. The properties of these groups will be elaborated in this chapter. We will also discuss three other groups obtained by incorporating ‘reflections’ into Zn, the dihedral group Dn, the generalized quaterion group Qn, and the dicyclic group...

Some Extreme Forms Defined in Terms of Abelian Groups

On the other hand, no one has yet constructed a sequence of forms for which yn{f) is unbounded, let alone of order n, as n -> oo. We have therefore thought it worthwhile to describe, in some detail, a new class of extreme forms yielding values yn{f) of order n% for suitable large n. More specifically, corresponding to each N = 2 (n = 2, 3, . . .) and to each sequence of integers Ao, Xv . . ., X...

Structural Properties of Inner Amenable Discrete Groups

Some New Results on the Chu Duality of Discrete Groups

This paper deals mainly with the Chu duality of discrete groups. Among other results, we give sufficient conditions for an FC group to satisfy Chu duality and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a group G coincide. As a consequence, it follows that when G is a weak sum of a family of finite simple groups, if the exponent of the groups in the family is bounded th...

Some Remarks on Non-discrete M Obius Groups

This paper contains some tentative steps towards describing the structure of non-discrete subgroups of SL(2; R). The main idea is that if a one-parameter family of groups G z varies analytically with the parameter z , then, using analytic continuation, certain results about discrete groups can be analytically continued to those groups in the family that are not discrete. The paper concentrates ...