How Groups Grow

Häftad, Engelska, 2011

Del 395 i serien London Mathematical Society Lecture Note Series

812 kr

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Beskrivning

Growth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory.

Produktinformation

Utgivningsdatum:2011-12-15
Mått:150 x 224 x 13 mm
Vikt:320 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Lecture Note Series
Antal sidor:210
Förlag:Cambridge University Press
ISBN:9781107657502

Utforska kategorier

Grupper och gruppteori inom Naturvetenskap och teknik

Mer om författaren

Avinoam Mann is a Professor Emeritus at his Alma Mater, the Einstein Institute of Mathematics in the Hebrew University of Jerusalem. He has published over a hundred papers on group theory and co-authored the influential book Analytic Pro-p Groups.

Recensioner i media

'How Groups Grow is an excellent introduction to growth of groups for everybody interested in this subject. It also touches a variety of adjacent subjects (such as amenability, isoperimetric inequalities, groups generated by automata, etc.) It is written in a very accessible style, with very clear exposition of all main results.' V. Nekrashevych, Bulletin of the American Mathematical Society

Innehållsförteckning

Preface; 1. Introduction; 2. Some group theory; 3. Groups of linear growth; 4. The growth of nilpotent groups; 5. The growth of soluble groups; 6. Linear groups; 7. Asymptotic cones; 8. Groups of polynomial growth; 9. Infinitely generated groups; 10. Intermediate growth: Grigorchuk's first group; 11. More groups of intermediate growth; 12. Growth and amenability; 13. Intermediate growth and residual finiteness; 14. Explicit calculations; 15. The generating function; 16. The growth of free products; 17. Conjugacy class growth; Research problems; References.