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We consider the linear stabilities of the regular n-gon relative equilibriaof the (1+n)-body problem. It is shown that there exist at most two kinds ofinfinitesimal bodies arranged alternatively at the vertices of a regular n-gonwhen n is even, and only one set of identical infinitesimal bodies when n isodd. In the case of n even, the regular n-gon relative equilibrium is shown tobe linearly stable when n>=14. In each case of n=8,10,12, linear stability canalso be preserved if the ratio of two kinds of masses belongs to an openinterval. When n is odd, the related conclusion on the linear stability isrecalled.

Linear stability of the n-gon relative equilibria of the (1+n)-body problem