We present new ALMA CO(2--1) observations of two well studied group-centered elliptical galaxies: NGC~4636 and NGC~5846. In addition, we include a revised analysis of Cycle 0 ALMA observations of the central galaxy in the NGC~5044 group that has been previously published. We find evidence that molecular gas, in the form of off-center orbiting clouds, is a common presence in bright group-centered galaxies (BGG). CO line widths are $gtrsim 10$ times broader than Galactic molecular clouds, and using the reference Milky Way $X_{CO}$, the total molecular mass ranges from as low as $2.6times 10^5 M_odot$ in NGC~4636 to $6.1times 10^7 M_odot$ in NGC~5044. With these parameters the virial parameters of the molecular structures is $gg 1$. Complementary observations of NGC~5846 and NGC~4636 using the ALMA Compact Array (ACA) do not exhibit any detection of a CO diffuse component at the sensitivity level achieved by current exposures. The origin of the detected molecular features is still uncertain, but these ALMA observations suggest that they are the end product of the hot gas cooling process and not the result of merger events. Some of the molecular clouds are associated with dust features as revealed by HST dust extinction maps suggesting that these clouds formed from dust-enhanced cooling. The global nonlinear condensation may be triggered via the chaotic turbulent field or buoyant uplift. The large virial parameter of the molecular structures and correlation with the warm ($10^3 - 10^5 K$)/hot ($ge10^6$) phase velocity dispersion provide evidence that they are unbound giant molecular associations drifting in the turbulent field, consistently with numerical predictions of the chaotic cold accretion process. Alternatively, the observed large CO line widths may be generated by molecular gas flowing out from cloud surfaces due to heating by the local hot gas atmosphere.
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