The order-types of central series
Published online by Cambridge University Press: 24 October 2008
Extract
Let
be a series of type Ω of the group G. By this we mean that Ω is an ordered set (we shall always understand ‘ordered’ to mean ‘totally ordered’) and Λσ and Vσ are subgroups of G satisfying
(i) Vσ ◃ Λσ for all σεΩ,
(ii) Λσ ≤ Vτ if σ < τ
(iii) , where G−1 denotes the set of elements ≠ 1 of G and Λσ−Vσ the set of elements of Λσ not belonging to Vσ,
(iv) Vσ ≠ Λσ for all σ ε Ω.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 2 , April 1965 , pp. 303 - 319
- Copyright
- Copyright © Cambridge Philosophical Society 1965
References
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