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Some varieties of groups

Published online by Cambridge University Press:  09 April 2009

M. F. Newman
Affiliation:
Australian National UniversityCanberra, ACT, 2600
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For positive integers n, c the class of groups all of whose n-generator subgroups are nilpotent of class (at most) c is a variety, here denoted [nc]. Hanna Neumann in her book ([15] pp. 93–98) reported on the first stage of the investigation of these varieties. The main result was that [nc] is nilpotent if and only if cn ≧ 2 ([15] 34.33 and 34.54).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1973

References

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