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The order-types of central series

Published online by Cambridge University Press:  24 October 2008

B. Hartley
B. Hartley
Affiliation:
Clare College, Cambridge
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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

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References

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