Discrete free products of two complex cyclic matrix groups
نویسندگان
چکیده
منابع مشابه
Discrete Free Products of Two Complex Cyclic Matrix Groups
Observe that the elements of ftxUf^ have infinite order, while those of ft2Uft3 have finite order. We will prove that whenever A e ft and B e ft do not both have a fixed point on L, then the group (A,B') is the discrete free product (A)*(B'), where B' denotes the transpose of B. The case where both A and B have a fixed point on L is also discussed. We show in addition that if A eft and Beft are...
متن کاملRandom walks on free products of cyclic groups
Let G be a free product of a finite family of finite groups, with the set of generators being formed by the union of the finite groups. We consider a transient nearest-neighbor random walk on G. We give a new proof of the fact that the harmonic measure is a special Markovian measure entirely determined by a finite set of polynomial equations. We show that in several simple cases of interest, th...
متن کاملOn the Cyclic Subgroup Separability of Free Products of Two Groups with Amalgamated Subgroup
Let G be a free product of two groups with amalgamated subgroup, π be either the set of all prime numbers or the one-element set {p} for some prime number p. Denote by Σ the family of all cyclic subgroups of group G, which are separable in the class of all finite π-groups. Obviously, cyclic subgroups of the free factors, which aren’t separable in these factors by the family of all normal subgro...
متن کاملCyclic Cohomology for Discrete Groups
We survey the cyclic cohomology associated with various algebras related to discrete groups. We then discuss the motivation and techniques of the cyclic theory approach to various problems in algebra and analysis.
متن کاملSpectra of Semidirect Products of Cyclic Groups
The spectrum of a graph is the set of eigenvalues of its adjacency matrix. A group, together with a multiset of elements of the group, gives a Cayley graph, and a semidirect product provides a method of producing new groups. This paper compares the spectra of cyclic groups to those of their semidirect products, when the products exist. It was found that many of the interesting identities that r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1979
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500003748