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Nilpotency and related properties of group extensions

Published online by Cambridge University Press:  17 April 2009

David Shield  and
Hanna Neumann
David Shield
Affiliation:
School of General Studies, Australian National University, Canberra, ACT.
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Abstract

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Gilbert Baums lag has given sufficient conditions for a group G to be nilpotent in terms of properties of a normal subgroup H and the quotient G/H, and has shown these conditions to be necessary when G is a wreath product and H its base group. His results are extended here to give corresponding conditions for weaker properties ranging from “bounded local nilpotency” to “being an Engel group”. Again we ask whether the sufficient conditions found are necessary when G is non-trivially a wreath product, or is of the form the answer is “yes” for the stronger properties considered, but for the weaker ones the question remains open.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 2 , April 1971 , pp. 145 - 154
Copyright
Copyright © Australian Mathematical Society 1971

References

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