In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence { x_n} such that { 0} \cup { \pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0; (ii) one of the subgroups { g \in G : 2g=0 and { g \in G : 3g=0} is open in G; (iii) G contains an open compact subgroup of the form Z_2^\kappa or Z_3^\kappa for some cardinal \kappa.
Categories: math.GN