Ranks of subgroups in boundedly generated groups. (Q2812008)

Let \(G\) be an \(m\)-boundedly generated group, and \(L\) a subgroup of finite index. If \(n\) is the exponent of \(L\) in \(G\), the author shows there is a further subgroup \(U\) of finite index in \(L\) such that rank of \(U\) is at most \(m\) and \([G:U]\leq n^m\).NEWLINENEWLINE The technique used here is based on the famous B. H. Neumann lemma; this was also employed by Nikolov and the reviewer earlier in the context of bounded generation. The author is able to deduce a surprisingly simple proof of a conjecture of Abert, Jaikin-Zapirain and Nikolov on the one hand, and also a variant of a conjecture of Lubotzky on the other.