Bieri‐Strebel Valuations (of Finite Rank)
Bieri‐Strebel Valuations (of Finite Rank)
复制标题
Bieri-Strebel 估值（有限秩）
DOI：
10.1112/plms/s3-52.2.269
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发表时间：
1986
影响因子：
1.8
通讯作者：
H. Aberg
中科院分区：
文献类型：
--
作者：
H. Aberg
页介绍269符号和术语271.基本事实2711.IM 2712的回顾2.AM 2733的回顾3.可解群、AG、有限Priifer秩、FP 2和HNN-扩展。276 4.有限秩下AM的矩阵计算。。。。2 775.有限条件：F、PM和有限表示。。。。278 6.m-驯化和w-驯化的性质280.证明了Hm{G，Y\rg)0蕴含m-驯化。。。。2811证明大纲2811.子模2822.子模内的可逆分式理想2833.‘fac’函数284.估计的雏形2875.通过hjg，f]rg的映射和一个相对的‘fac’.。。。2 8 8 6.可逆分数理想的估计288 7.估计290 8.v的上界291 9.主要定理292 10.最终陈述293 III.证明w-tame蕴含F P m 293轮廓和证明的开始2931.约化为平凡扩张294 2.空间Y的构造和群^295 3.Y的w-连通性的计算IV.结论301 1.亚可解群301 2.可解群302参考303
Page Introduction 269 Notation and terminology 271 I. Basic facts 271 1. Review of IM 271 2. Review of AM 273 3. Solvable groups, aG, finite Priifer rank, FP 2 , and HNN-extensions . 276 4. Matrix computation of AM in the finite rank case . . . . 277 5. Finiteness conditions: F P m and finite presentation . . . . 278 6. The properties m-tameness and w-domestication 280 II. Proof that Hm{G, Y\ RG) zero implies m-domestication . . . . 2 8 1 Outline of proofs 281 1. The submodule 282 2. Invertible fractional ideals inside the submodule 283 3. The 'fac' function 284 4. Rudiments of an estimate 287 5. A map through HJG, f ] RG) and a relative 'fac' . . . . 2 8 8 6. The estimate for invertible fractional ideals 288 7. The estimate 290 8. Upper bound for v 291 9. Main theorem 292 10. Final statement 293 III. Proof that w-tame implies F P m 293 Outline and start of proofs 293 1. Reduction to trivial extensions 294 2. Construction of the space Y, and the group ^ 295 3. Computat ion of the w-connectedness of Y 299 IV. Conclusion 301 1. Metabelian groups 301 2. Solvable groups 302 References 303