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The deficiency and the multiplicator of finite nilpotent groups

Published online by Cambridge University Press:  09 April 2009

J. W. Wamsley
J. W. Wamsley
Affiliation:
The Flinders University of South Australia
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I. Šafarevič [2] proves that for a pro-finite p-group G, the deficiency of G (in the topological sense) equals the negative of d(m(G)). This means that if G is a finite p-group, where d(m(G)) = n, then there exists a group K with deficiency −n, such that G is the maximal p factor of K.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 124 - 128
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Lyndon, R. C., ‘Cohomology theory of groups with a single defining relation’, Annals of Math. (2) 52 (1950), 650–665.CrossRefGoogle Scholar
[2]Šafarevič, I. R., ‘Extensions with prescribed branch points’, Inst. Hautes 'Etudes Sci. Pub!. Math. No. 18 (1963), 71–95;Google Scholar
Translations Amer. Math. Soc., Ser. 2, Vol. 59, 128–149.Google Scholar