John C. Lennox and Derek J. S. Robinson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.001.0001
- Subject:
- Mathematics, Pure Mathematics
This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev ...
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This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev completions, soluble linear groups, P. Hall’s theory of finitely generated soluble groups, soluble groups with finite rank, soluble groups whose abelian subgroups satisfy finiteness conditions, simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, centrality in finitely generated soluble groups and the Lennox-Roseblade theorem, algorithmic problems for polycyclic and metabelian groups, cohomological topics including groups with finite (co)homological dimension and vanishing theorems, finitely presented soluble groups, constructible soluble groups, the Bieri-Strebel invariant, subnormality, and soluble groups.Less
This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev completions, soluble linear groups, P. Hall’s theory of finitely generated soluble groups, soluble groups with finite rank, soluble groups whose abelian subgroups satisfy finiteness conditions, simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, centrality in finitely generated soluble groups and the Lennox-Roseblade theorem, algorithmic problems for polycyclic and metabelian groups, cohomological topics including groups with finite (co)homological dimension and vanishing theorems, finitely presented soluble groups, constructible soluble groups, the Bieri-Strebel invariant, subnormality, and soluble groups.
John C. Lennox and Derek J. S. Robinson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.003.0001
- Subject:
- Mathematics, Pure Mathematics
This chapter provides an introduction to soluble and nilpotent groups. It discusses the properties of the upper and lower central series and talks about polycyclic groups and Cernikov groups.
This chapter provides an introduction to soluble and nilpotent groups. It discusses the properties of the upper and lower central series and talks about polycyclic groups and Cernikov groups.
