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A Frattini-like subgroup

Published online by Cambridge University Press:  24 October 2008

M. J. Tomkinson
M. J. Tomkinson
Affiliation:
Mathematics Dept., University of Glasgow
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Extract

The Frattini subgroup φ(G) of a group G is the intersection of G and all its maximal subgroups. The following results for finite groups are well known:

THEOREM A0. If G is a finite group, then the following three conditions are equivalent:

(i) G is nilpotent,

(ii) G/φ(G) is nilpotent,

(iii) φ(G) ≥ G′.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 247 - 257
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

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