On automorphism group of a possible short algorithm for multiplication of $3\times3$ matrices
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 $l\leq22$ for multuplication of $3\times3$ matrices then its automorphism group is isomorphic to a subgroup of $S_l\times S_3$.
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