On automorphism group of a possible short algorithm for multiplication of 3×3 matrices

11/11/2022

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by   Vladimir Burichenko, et al.

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Studying algorithms admitting nontrivial symmetries is a prospective way of constructing new short algorithms of matrix multiplication. The main result of the article is that if there exists an algorithm of multiplicative length l≤22 for multuplication of 3×3 matrices then its automorphism group is isomorphic to a subgroup of S_l× S_3.