On Certain C-Test Words for Free Groups

On Certain C-test Words for Free Groups

Abstract. Let Fm be a free group of a finite rank m ≥ 2 and Xi, Yj be elements in Fm. A nonempty word w(x1, . . . , xn) is called a C-test word in n letters for Fm if, whenever w(X1, . . . ,Xn) = w(Y1, . . . , Yn) 6= 1, the two n-tuples (X1, . . . , Xn) and (Y1, . . . , Yn) are conjugate in Fm. In this paper we construct, for each n ≥ 2, a C-test word vn(x1, . . . , xn) with the additional prop...

Symmetric Random Walks on Certain Amalgamated Free Product Groups

We consider nearest–neighbor random walks on free products of finitely many copies of the integers with amalgamation over nontrivial subgroups. When all the subgroups have index two, we find the Green function of the random walks in terms of complete elliptic integrals. Our technique is to apply Voiculescu’s operator–valued R–transform.

On C∗-Algebras Associated to Certain Endomorphisms of Discrete Groups

Let α : G → G be an endomorphism of a discrete amenable group such that [G : α(G)] < ∞. We study the structure of the C∗ algebra generated by the left convolution operators acting on the left regular representation space, along with the isometry of the space induced by the endomorphism.

On Certain Groups of Functions

Let C(X,G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups A(X) of C(X,G) of the M {f C(X,G): f(p) e} which is P analogous to the hull-kernel topology on the commutative Banach algegra C(X) of all continuou...

Isomorphism Classes and Derived Series of Certain Almost-Free Groups