The 2-length of the Hughes subgroup
The (generalized) Hughes subgroup \(H_{p\quad n}(G)\) of a finite group G (p a prime, \(n\geq 1)\) is defined as the subgroup of G generated by all elements x such that \(x^{p\quad n}\neq 1\). It is conjectured that for finite solvable G with \(1\neq H:=H_{p\quad n}(G)\neq G\) the Fitting length of H is bounded by n, generalizing the Kegel-Hughes-Thompson theorem \((n=1)\). For odd primes p, the conjecture was proved by Espuelas improving weaker results by various authors. In the reviewed paper, the author proves that for \(p=2\) at least the 2-length of H is bounded by n.
scientific article; zbMATH DE number 4063364