Measurement of branching fractions and charge asymmetries in B+ decays to ηπ+, ηk+, ηρ+, and η′π+, and search for B0 decays to ηk0 and ηω

We present measurements of branching fractions and charge asymmetries for six B-meson decay modes with an η or η′ meson in the final state. The data sample corresponds to 232×106 BB̄ pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- B Factory at SLAC. We measure the branching fractions (in units of 10-6): B(B+→ηπ+)=5. 1±0.6±0.3, B(B+→ηK+)=3.3±0.6±0.3, B(B0→ηK0)=1.5±0.7±0.1 (<2.5 at 90% C.L.), B(B+→ηρ+)=8.4±1.9±1.1, B(B0→ηω)=1. 0±0.5±0.2 (<1.9 at 90% C.L.), and B(B+→η′π+)= 4.0±0.8±0.4, where the first uncertainty is statistical and second systematic. For the charged modes we also determine the charge asymmetries, all found to be compatible with zero.