Relation Modules of Infinite Groups |
| |
Authors: | Evans Martin J |
| |
Institution: | Department of Mathematics, University of Alabama Tuscaloosa, AL 35487, USA |
| |
Abstract: | Let Fn be the free group of rank n with basis x1, x2, ..., xn,and let d(G) denote the minimal number of generators of thefinitely generated group G. Suppose that n d(G). There existsan exact sequence
and wemay view the free abelian group as a right ZG-module by defining (rR')g = rg 1R' for allg G, where g 1 is any preimage of g under , and = (g 1)1 r(g 1),the conjugate of r by g 1. We call the relation module of G associated with the presentation(1), and say that has ambient rank n. Furthermore, we call the group Fn/R' the free abelianizedextension of G associated with (1). 1991 Mathematics SubjectClassification 20F05, 20C07. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|