** Speaker:** John Shareshian, Washington University in St. Louis

** Title:** Subrack lattices of group racks

** Abstract: ** In joint work with Istvan Heckenberger and Volkmar Welker, we
study subrack lattices of group racks. The operation a.b=aba^{-1} makes a
group G a rack. The subracks of this rack are those subsets of G that are
closed under conjugation. The inclusion partial order makes the set of
subracks of G a lattice. Assuming that G is finite, we show that the
combinatorial structure of the subrack lattice of G is closely related to
the algebraic structure of G. Indeed, if G and H have isomorphic subrack
lattices and G is abelian, then H is also abelian. The claim of the
previous sentence remains true if we replace "abelian" with "nilpotent",
"supersolvable", "solvable" or "simple".