\({\mathfrak F}\)-projectors in locally finite groups (Q1090417)

In [J. Algebra 76, 192-204 (1982; Zbl 0482.20023)] the author considered formations in the class \({\mathfrak X}\) of countable locally finite-soluble groups satisfying min-p for all primes p. He proved that if \({\mathfrak F}\) is a cohopfian saturated formation then every \({\mathfrak X}\)-group G has \({\mathcal F}\)-projectors. (A formation \({\mathfrak F}\) is cohopfian if no \({\mathfrak F}\)-group has a proper subgroup isomorphic to itself.) Also if H, K are two \({\mathfrak F}\)-projectors of the \({\mathfrak X}\)-group G, then, for each finite set \(\sigma\) of primes, the Sylow \(\sigma\)-subgroups of H are conjugate to those of K. Here it is shown that the \({\mathfrak F}\)-projectors of G are conjugate if and only if G has only countably many \({\mathfrak F}\)- projectors.