THE a-CONCENTRATION OF PROCACCIA OF INFINITE WORDS IN FINITELY GENERATED FUCHSIAN GROUPS
نویسنده
چکیده
In order to study the spectral decomposition (a,f(a» of Procaccia of the limit set L(G) of a finitely generated Fuchsian group G of rigid movements in the hyperbolic half plane IH, it is necessary to calculate the a of each element of L(G). Each such element is an allowed infinite word, each letter a generator of G. In this paper we calculate first the 0' of the periodic infinite words, and use this result in order to calculate the 0' of the non-periodic irrational words. SECTIO]\"
منابع مشابه
On trivial ends of Cayley graph of groups
In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...
متن کاملAlternating Quotients of Fuchsian Groups
It all started with a theorem of Miller [14]: the classical modular group PSL2Z has among its homomorphic images every alternating group, except A6; A7; and A8. In the late 1960s Graham Higman conjectured that any (finitely generated non-elementary) Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This reduces to an investigation of the cocompac...
متن کاملOn finitely generated modules whose first nonzero Fitting ideals are regular
A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of $R^n$ which is generated by columns of a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set. ...
متن کاملFully Residually Free Groups and Graphs Labeled by Infinite Words
Let F = F (X) be a free group with basis X and Z[t] be a ring of polynomials with integer coefficients in t. In this paper we develop a theory of (Z[t], X)-graphs a powerful tool in studying finitely generated fully residually free (limit) groups. This theory is based on the Kharlampovich-Myasnikov characterization of finitely generated fully residually free groups as subgroups of the Lyndon’s ...
متن کاملWeakly Finitely Presented Infinite Periodic Groups
A group G given by a presentation G = 〈A ‖ R〉 is called weakly finitely presented if every finitely generated subgroup of G, generated by (images of) some words in A, is naturally isomorphic to the subgroup of a group G0 = 〈A0 ‖ R0〉, where A0 ⊆ A, R0 ⊆ R are finite, generated by (images of) the same words. In the article, weakly finitely presented periodic groups which are not locally finite ar...
متن کامل