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We address the problem of studying the toric ideals of phylo- genetic invariants for a general group-based model on an arbitrary claw tree. We focus on the group Z2 and choose a natural recursive approach that extends to other groups. The study of the lattice associated with each phylogenetic ideal produces a list of circuits that generate the corre- sponding lattice basis ideal. In addition, we describe explicitly a quadratic lexicographic Grobner basis of the toric ideal of invariants for the claw tree on an arbitrary number of leaves. Combined with a result of Sturm- fels and Sullivant, this implies that the phylogenetic ideal of every tree for the group Z2 has a quadratic Grobner basis. Hence, the coordinate ring of the toric variety is a Koszul algebra.

Toric Ideals of Phylogenetic Invariants for the General Group-Based Model on Claw Trees K 1,n