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Local theorems and group extensions

Published online by Cambridge University Press:  24 October 2008

Kenneth K. Hickin  and
Richard E. Phillips
Kenneth K. Hickin
Affiliation:
Michigan State University
Richard E. Phillips
Affiliation:
Michigan State University
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Extract

The concept of a local system of a set W is defined in ((8), p. 166) and ((12), p. 126). Recall that a set ℒ of subsets of W is a local system if Uℒ = W and ℒ is directed in the following sense: for every finite set H1, …, Hn of elements of ℒ, there is an M∈ℒ such that Hi⊂M for 1≤i≤n. If Σ is a class of groups, L(Σ) is the class of all groups G that possess a local system of Σ subgroups. Σ satisfies the local theorem, or is L-closed, if L(Σ)⊂Σ. Many classes of groups which satisfy the local theorem are discussed in ((12), pp. 126–144).

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 7 - 20
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

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