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On prime-power groups in which the derived group has two generators

Published online by Cambridge University Press:  24 October 2008

N. Blackburn
N. Blackburn
Affiliation:
Trinity CollegeCambridge
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Extract

Burnside ((1), p. 241) has proved the following theorem:

If G is a non-metabelian p-group, then the centre of the derived group of G cannot be cyclic. In particular, a non-Abelian group of order p3 cannot be the derived group of a p-group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 19 - 27
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Burnside, W.On some properties of groups whose orders are powers of primes. Proc. Lond. Math. Soc. (2) 11 (1912), 225–45.Google Scholar
(2)Hall, P.A contribution to the theory of groups of prime-power order. Proc. Lond. Math. Soc. (2) 36 (1933), 29–95.Google Scholar
(3)Huppert, B.Über das Produkt von paarweise vertauschbaren zyklischen Gruppen. Math. Z. 58 (1953), 243–64.CrossRefGoogle Scholar
(4)Wiman, A.Über p–Gruppen von maximaler Klasse. Acta Math., Stockh., 88 (1952), 317–46.CrossRefGoogle Scholar
(5)Zassenhaus, H.Lehrbuch der Gruppentheorie (Leipzig-Berlin, 1937).Google Scholar
(6)Itô, N.Über das Produkt von zwei abelschen Gruppen. Math. Z. 62 (1955), 400–1.CrossRefGoogle Scholar