Let G be a countable locally finite group satisfying min-p for all primes p. Then G is the fitting subject of a question originally asked by Baer of locally finite-soluble groups with finite Sylow subgroups. If G contains no proper subgroup isomorphic to itself, is G hyperfinite? We answer this question in the affirmative; this has already been shown by Beljaev when G is locally soluble. We investigate further the properties of G, given that G is not hyperfinite. If this is the case, then G can be embedded in each of a large number of nonisomorphic locally finite groups, so that G contains a conjugate of each finite subgroup of these overgroups. In addition, we include a note on fixed point free action of finite groups in the non-coprime case.