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Subgroup Growth.
・ISBN 978-3-7643-6989-7 hard EUR 49.99
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| 著者・編者 | Lubotzky, Alexander / Segal, Dan, |
|---|---|
| シリーズ | (Progress in Mathematics) |
| 出版社 | (Birkhauser Verlag AG, SZ) |
| 出版年月 | 2003 |
| ページ数 | 454 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A05-41560＞ |
解説
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'.