Abstract
In connection with the class field theory a problem concerning p-groups was proposed by W. Magnus: Is there any infinite tower of p-groups G1, G2,…, Gn, Gn+1,…such that G1 is abelian and each Gn is isomorphic to Gn+1/θn(Gn+1), θn(Gn+1) ≠ 1, n = 1,2,…, where θn(Gn+1) denotes the n-th commutator subgroup of Gn+1? The present note is, firstly, to construct indeed such a tower, to settle the problem, and also to refine an inequality for p-groups of P. Hall.
Publisher
Cambridge University Press (CUP)
Reference2 articles.
1. A contribution to the theory of groups of prime power order;Hall;Proc. London Math. Soc.,1934
2. Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring
Cited by
4 articles.
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