  We present stellar parameters and abundances of 11 elements (Li, Na, Mg, Al,
Si, Ca, Ti, Cr, Fe, Ni, and Zn) of 13 F6-K2 main-sequence stars in the young
groups AB Doradus, Carina Near, and Ursa Major. The exoplanet-host star \iota
Horologii is also analysed.
  The three young associations have lithium abundance consistent with their
age. All other elements show solar abundances. The three groups are
characterised by a small scatter in all abundances, with mean [Fe/H] values of
0.10 (\sigma=0.03), 0.08 (\sigma=0.05), and 0.01 (\sigma=0.03) dex for AB
Doradus, Carina Near, and Ursa Major, respectively. The distribution of
elemental abundances appears congruent with the chemical pattern of the
Galactic thin disc in the solar vicinity, as found for other young groups. This
means that the metallicity distribution of nearby young stars, targets of
direct-imaging planet-search surveys, is different from that of old, field
solar-type stars, i.e. the typical targets of radial velocity surveys.
  The young planet-host star \iota Horologii shows a lithium abundance lower
than that found for the young association members. It is found to have a
slightly super-solar iron abundance ([Fe/H]=0.16+-0.09), while all [X/Fe]
ratios are similar to the solar values. Its elemental abundances are close to
those of the Hyades cluster derived from the literature, which seems to
reinforce the idea of a possible common origin with the primordial cluster.
