Subgroup Growth by Alexander Lubotzky, Dan Segal
  

Synopsis

Subgroup Growth by Alexander Lubotzky, Dan Segal

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.

Reviews

Subgroup Growth is an extremely well-written book and is a delight to read. It has a wealth of information making a rich and timely contribution to an emerging area in the theory of groups which has come to be known as Asymptotic Group Theory. This monograph and the challenging open problems with which it concludes are bound to play a fundamental role in the development of the subject for many years to come. -Journal Indian Inst of Science [Subgroup growth] is one of the first books on Asymptotic Group Theory - a new, quickly developing direction in modern mathematics...The book of A. Lubotzky and D.Segal, leading specialists in group theory, answers...questions in a beautiful way ...It was natural to expect a text on the subject that would summarize the achievements in the field and we are very lucky to witness the appearance of this wonderful book. ...Readers will be impressed with the encyclopedic scope of the text. It includes all, or almost all, topics related to subgroup growth ...The book also includes plenty of general information on topics that are well known to algebraic audiences and should be part of the background for every modern researcher in mathematics. ...a wonderful methodological tool introduced by the authors. ... The book ends [with] a section on open problems, which contains 35 problems related to subgroup growth. The list will be useful and interesting to both established mathematicians and young researchers. There is no doubt that the list includes the most important and illuminating problems in the area, and we eagerly anticipate solutions of at least some of them in the near future. The book will surely have [a] big impact on all readers interested in Group Theory, as well as in Algebra and Number Theory in general. -Bulletin of the AMS The proofs in this book employ a remarkable variety of tools, from all branches of group theory, certainly, but also from number theory, logic, and analysis... The authors supply surveys, and some proofs, of necessary results, in the windows at the end of the book. These comprise about one quarter of the full book, and they give the needy reader a handy reference, without interrupting the flow of argument in the main text... Since the subject of this book is an active area of current research, there are many open problems in it... -Mathematical Reviews

About the Author

Other Formats

Book Info

Format

Paperback
454 pages

Author

Alexander Lubotzky, Dan Segal
More books by Alexander Lubotzky, Dan Segal

Publisher

Springer Basel

Publication date

21st August 2012

ISBN

9783034898461


I love Lovereading because I often never know what to read and this helps you find a good book. I have recommended this to many people.

Shannon-Louise Masters – age 15

You give me age appropriate ideas of books I can read and buy for the children and find out what other children their age think of them too.

Katie Lonsdale

This company is amazing; not only is it is a great opportunity to get books and review them but everyone is so friendly and supportive!

Jemma Rubens, age 10

I have told all my friends, family & teachers to see for themselves just how great the site is. Without fail, they are hugely impressed.

Alexander Boxall – age 11

It gives me a chance to read types of books that I would not normally try, and it motivates me to read every night to finish it!

Alice Horncastle, age 14

I am so pleased to have signed my kids up as they are reading a much wider range of books and even choosing books out of their comfort zone.

Angela East

We love Lovereading4kids because it promotes reading choices, new authors and a sense of community for children of all ages!

Rachel Bridgeman

It is THE website to use for narrowing down your search for any book. Definitely knocks the socks off any other book review website.

Nickey and Tomasz Hawryszczuk
Lovereading

Lovereading 4 schools