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We discuss the merging rates in compact groups of 5 identical ellipticalgalaxies. All groups have the same mass and binding energy. We consider bothcases with individual halos and cases where the halo is common to all galaxiesand enveloping the whole group. In the latter situation the merging rate isslower if the halo is more massive. The mass of individual halos has littleinfluence on the merging rates, due to the fact that all galaxies in oursimulations have the same mass, and so the more extended ones have a smallervelocity dispersion. Groups with individual halos merge faster than groups withcommon halos if the configuration is centrally concentrated, like a Kingdistribution of index 10. On the other hand for less concentratedconfigurations the merging is initially faster for individual halo cases, andslower after part of the group has merged. In cases with common halo, centrallyconcentrated configurations merge faster for high halo-to-total mass ratios andslower for low halo-to-total mass ratios. Groups whose virial ratio isinitially less than one merge faster, while groups that have initiallycylindrical rotation merge slower than groups starting in virial equilibrium.In order to test how long a virialised group can survive before merging wefollowed the evolution of a group with a high halo-to-total mass ratio and adensity distribution with very little central concentration. We find that thefirst merging occurred only after a large number of crossing times, which withareasonable calibration should be larger than a Hubble time. Hence, at leastfor appropriate initial conditions, the longevity of compact groups is notnecessarily a problem, which is an alternative explanation to why we observe somany compact groups despite the fact that their lifetimes seem short.Comment: 15 pages Latex, with 12 figures included, requires mn.sty, accepted  for publication in MNRA

Evolution of compact groups of galaxies -- I. Merging rates