The Theory of Infinite Soluble GroupsClarendon Press, 19 août 2004 - 360 pages The central concept in this monograph is that of a soluble group - a group which is built up from abelian groups by repeatedly forming group extensions. It covers all the major areas, including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, and finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory. An up-to-date survey of the area aimed at research students and academic algebraists and group theorists, it is a compendium of information that will be especially useful as a reference work for researchers in the field. |
Table des matières
| 1 | |
2 Nilpotent groups | 29 |
3 Soluble linear groups | 47 |
4 The theory of finitely generated soluble groups I | 60 |
5 Soluble groups of finite rank | 83 |
6 Finiteness conditions on abelian subgroups | 105 |
7 The theory of finitely generated soluble groups II | 121 |
8 Centrality in finitely generated soluble groups | 143 |
9 Algorithmic theories of finitely generated soluble groups | 158 |
10 Cohomological methods in infinite soluble group theory | 191 |
11 Finitely presented soluble groups | 240 |
12 Subnormality and solubility | 275 |
Bibliography | 290 |
| 335 | |
| 338 | |
Expressions et termes fréquents
abelian group abelian normal subgroup abelian subgroup acts addition algebraic algorithm apply argument ascending assume automorphism called clearly commutators complete condition conjugate Consequently consider constructible contains contradiction course deduce define denote derived length direct elements establish example exists extension fact factors Finally finite index finite rank finitely generated soluble finitely presented follows free abelian further given group G Hence homomorphism hypothesis ideal implies induction infinite integer isomorphic Let G linear locally Math maximal metabelian group minimal module nilpotent group non-trivial normal subgroup observe obtain p-group polycyclic group positive prime problem Proof prove quotient R-module radicable rank reduced relations residually finite result ring Robinson satisfies sequence simple soluble groups structure subgroup of G submodule subnormal subset Suppose theorem theory torsion-free trivial true write ZG-module