On groups of polynomial subgroup growth |
| |
Authors: | Alexander Lubotzky Avinoam Mann |
| |
Institution: | (1) Institute of Mathematics, Hebrew University, 91904 Jerusalem, Israel |
| |
Abstract: | Summary Let be a finitely generated group anda
n
( )=the number of its subgroups of indexn. We prove that, assuming is residually nilpotent (e.g., linear), thena
n
( ) grows polynomially if and only if is solvable of finite rank. This answers a question of Segal. The proof uses a new characterization ofp-adic analytic groups, the theory of algebraic groups and the Prime Number Theorem. The method can be applied also to groups of polynomial word growth.Oblatum 1-VII-1989 & 7-VI-1990 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|