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.
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