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A Commutator Formula for a Pair of Subgroups and A Theorem of Blackburn

Published online by Cambridge University Press:  20 November 2018

Tsit-Yuen Lam
Tsit-Yuen Lam*
Affiliation:
University of California, BerkeleyCalifornia 94720
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Let be the lower central series of a group G, where K2(G) = [G, G] and inductively Kn+1(G) = [Kn (G), G]. A theorem of Blackburn ([1], Hilfssatz) states that

Theorem 1. The exponent of Kn+1 (G)/Kn+2 (G) divides the exponent of Kn (G)/Kn+1 (G).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 217 - 219
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Blackburn, N., Über das Produkt von zwei zyklischen 2-Gruppen. Math. Z. 68 (1958) 422–427.Google Scholar