科研之友
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摘要
For any finite group G and a positive integer m, we define and study a Schur ring over the direct power G(m), which gives an algebraic interpretation of the partition of G(m) obtained by the m-dimensional Weisfeiler-Leman algorithm. It is proved that this ring determines the group G up to isomorphism if m = 3, and approaches the Schur ring associated with the group Aut(G) acting on G(m) naturally if m increases. It turns out that the problem of finding this limit ring is polynomial-time equivalent to the group isomorphism problem.
