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Some varieties of groups

Published online by Cambridge University Press:  09 April 2009

M. F. Newman
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 [n → c]. 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 [n → c] is nilpotent if and only if c ≦ n ≧ 2 ([15] 34.33 and 34.54).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 481 - 494
Copyright
Copyright © Australian Mathematical Society 1973

References

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