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Wreath products and p–groups

Published online by Cambridge University Press:  24 October 2008

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
Department of MathematicsThe UniversityManchester 13
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Extract

The wreath product is a useful method for constructing new soluble groups from given ones (cf. P. Hall (3)). Now although the wreath product of one soluble group by another is (obviously) always soluble, the corresponding result is no longer true for nilpotent groups. It is the object of § 3 of this note to determine precisely when the wreath product W of a non-trivial nilpotent group A by a non-trivial nilpotent group B is nilpotent; in fact I prove that W is nilpotent if and only if both A and B are (nilpotent) p–groups with A of finite exponent and B finite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 3 , July 1959 , pp. 224 - 231
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

(1)Čeknikov, S. N.Complete groups with an ascending centrai series. Mat. Sbornik, 18 (1946), 397–422.Google Scholar
(2)Hall, P.A contribution to the theory of groups of prime-power order. Proc. Lond. Math. Soc. 36 (1933) 29–95.Google Scholar
(3)Hall, P.Finiteness conditions for soluble groups. Proc. Lond. Math. Soc. (3), 4 (1954), 419–36.Google Scholar
(4)Kurosh, A. G.The theory of groups, vols. 1 and 2 (New York, 1956).Google Scholar
(5)Mal'cev, A. I.Nilpotent torsion-free groups. Izv. Akad. Nauk. SSSR. Ser. Mat. 13 (1949), 201–12.Google Scholar
(6)Neumann, B. H.Adjunotion of elements to groups. J. Lond. Math. Soc. 18 (1943), 12–20.CrossRefGoogle Scholar
(7)Schmidt, O. J.On infinite special groups. Mat. Sbornik, 8 (1940), 363–75.Google Scholar
(8)Baumslag, G. Some aspects of groups with unique roots. (To appear Acta math., Stockh.)Google Scholar