Aims: To gain better insight on the physics of stripped-envelope core-collapse supernovae through studying their environments. Methods: We obtained low-resolution optical spectroscopy with the New Technology Telescope (+ EFOSC2) at the locations of 20 Type Ib/c supernovae. We measure the flux of emission lines in the stellar-continuum-subtracted spectra from which local metallicities are computed. For the supernova regions we estimate both the mean stellar age, interpreting the stellar absorption with population synthesis models, and the age of the youngest stellar populations using the H-alpha equivalent width as an age indicator. These estimates are compared with the lifetimes of single massive stars. Results: Based on our sample, we detect a tentative indication that Type Ic supernovae might explode in environments that are more metal-rich than those of Type Ib supernovae (average difference of 0.08 dex), but this is not a statistically significant result. The lower limits placed on the ages of the supernova birthplaces are overall young, although there are several cases where these appear older than what is expected for the evolution of single stars more massive than 25-30 M_{sun}. This is only true, however, assuming that the supernova progenitors were born during an instantaneous (not continuous) episode of star formation. Conclusions: These results do not conclusively favor any of the two evolutionary paths (single or binary) leading to stripped supernovae. We do note a fraction of events for which binary evolution is more likely, due to their associated age limits. The fact, however, that the supernova environments contain areas of recent (< 15 Myr) star formation and that the environmental metallicities are, at least, not against the single evolutionary scenario, suggest that this channel is also broadly consistent with the observations.
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