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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

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