Download e-book for iPad: Algebraic Generalizations of Discrete Groups: A Path to by Benjamin Fine

By Benjamin Fine

ISBN-10: 0824703197

ISBN-13: 9780824703196

A survey of one-relator items of cyclics or teams with a unmarried defining relation, extending the algebraic examine of Fuchsian teams to the extra common context of one-relator items and comparable workforce theoretical issues. It offers a self-contained account of yes typical generalizations of discrete teams.

Show description

Read Online or Download Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products PDF

Similar group theory books

Read e-book online Group Theory for Physicists PDF

This textbook explains the elemental techniques and strategies of crew conception by way of utilizing language typical to physicists. software the way to physics are emphasised. New fabrics drawn from the instructing and examine event of the writer are integrated. This booklet can be utilized by means of graduate scholars and younger researchers in physics, specifically theoretical physics.

Oligomorphic Permutation Groups - download pdf or read online

The learn of permutation teams has continually been heavily linked to that of hugely symmetric buildings. The gadgets thought of listed below are countably limitless, yet have simply finitely many various substructures of any given finite dimension. they're accurately these buildings that are decided via first-order logical axioms including the belief of countability.

Extra resources for Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products

Example text

Surv. 356 (2004), No. 2, 65–104. [70] F. O. Wagner, Relational structures and dimensions, pp. 153–180 in Automorphisms of First-Order Structures (ed. R. W. Kaye and H. D. Macpherson), Oxford University Press, Oxford, 1994. [71] H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. [72] H. Wielandt, Unendliche Permutationsgruppen, Lecture Notes, Universit¨ at T¨ ubingen, 1959. [English translation by P. Bruyns included in Wielandt’s collected works: H. edu Contents 1 Self-similar objects 38 2 Actions on rooted trees 41 3 Self-similar groups 44 4 Iterated monodromy groups 50 5 Branch groups 56 6 Growth of groups 66 7 Amenability 72 8 Schreier graphs related to self-similar groups 81 Introduction The idea of self-similarity is one of the most basic and fruitful ideas in mathematics of all times and populations.

4n 3 What happens for primitive groups? The first result asserts the existence of a wide gap, between constant and exponential growth. /p(n) for some polynomial p. 148 . .. 324 . .. No counterexamples are known to the conjecture that both parts hold with c = 2. The growth rates of the sequences (fn ) and (Fn ) appear to have a great deal of structure; little is known, but examples suggest some conjectures. One of the most challenging conjectures is to prove that various ‘obvious’ limits, such as lim(log fn )/(log n) (for polynomial growth), lim(log log fn )/(log n) (for fractional exponential growth), or lim(log fn )/n (for exponential growth), actually exist.

Self-similarity and branching in group theory Grigorchuk, Suni c 44 Definition 3 The homomorphism ϕu is called the projection of G at u. The image of ϕu is denoted by Gu and called the upper companion group of G at u. The map ψn : StG (Ln ) → Aut(T ) u∈Ln given by ψn (g) = (ϕu (g))u∈Ln = (gu )u∈Ln is a homomorphism. We usually omit the index in ψn when n = 1. In the case of G = Aut(T ) the maps ϕu : StAut(T ) (u) → Aut(T ) and ψn : StAut(T ) (Ln ) → u∈Ln Aut(T ) are isomorphisms, for any word u over X and any n ≥ 0.

Download PDF sample

Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products by Benjamin Fine

by Richard

Rated 4.49 of 5 – based on 40 votes