Normal growth of large groups. II. (Q1777334)

The authors write that the proof of Theorem 1 of part I [ibid. 81, No. 6, 609-613 (2003; Zbl 1051.20013)] turns out to be incorrect. They have not been able to remedy the proof of this Theorem 1. The authors give the following slightly weaker result. Let \(A\) be a finitely generated group, possessing a normal finite index subgroup \(B\) which maps surjectively onto a group \(G\) such that the pro-\(p\) completion of \(G\) is a non-Abelian free pro-\(p\) group for some prime \(p\) not dividing \((A:B)\). Then \(S_n^ \triangleleft(A)\) is of type \(n^{\log n}\). Here \(S_n^\triangleleft(A)\) is the number of normal subgroups of index \(\leq n\).