Associations of dwarf galaxies are loose systems composed exclusively of dwarf galaxies. These systems were identified in the Local Volume for the first time more than thirty years ago. We study these systems in the cosmological framework of the $Lambda$ Cold Dark Matter ($Lambda$CDM) model. We consider the Small MultiDark Planck simulation and populate its dark matter haloes by applying the semi-analytic model of galaxy formation SAG. We identify galaxy systems using a friends of friends algorithm with a linking length equal to $b=0.4 ,{rm Mpc},h^{-1}$, to reproduce the size of dwarf galaxy associations detected in the Local Volume. Our samples of dwarf systems are built up removing those systems that have one (or more) galaxies with stellar mass larger than a maximum threshold $M_{rm max}$. We analyse three different samples defined by ${rm log}_{10}(M_{rm max}[{rm M}_{odot},h^{-1}]) = 8.5, 9.0$ and $9.5$. On average, our systems have typical sizes of $sim 0.2,{rm Mpc},h^{-1}$, velocity dispersion of $sim 30 {rm km,s^{-1}} $ and estimated total mass of $sim 10^{11} {rm M}_{odot},h^{-1}$. Such large typical sizes suggest that individual members of a given dwarf association reside in different dark matter haloes and are generally not substructures of any other halo. Indeed, in more than 90 per cent of our dwarf systems their individual members inhabit different dark matter haloes, while only in the remaining 10 per cent members do reside in the same halo. Our results indicate that the $Lambda$CDM model can naturally reproduce the existence and properties of dwarf galaxies associations without much difficulty.
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