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On prime-power groups with two generators

Published online by Cambridge University Press:  24 October 2008

N. Blackburn
N. Blackburn
Affiliation:
Trinity CollegeCambridge
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Extract

Let G denote a group of order a power of the prime p, and let G′ be the derived group of G. The lower central series of G will be written

For any subgroup H of G we denote by P(H) the subgroup of H generated by all elements xp as x runs through H, and by Φ(H) the Frattini subgroup of H. We write (H:Φ(H)) = pd(H); thus d(H) is the minimal number of generators of H.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 3 , July 1958 , pp. 327 - 337
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

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