Proves the automorphism group's structure for short matrix multiplication algorithms, indicating potential symmetries in design.
The study of algorithms admitting nontrivial symmetries is a promising way to find new short matrix multiplication algorithms. It is proved that the automorphism group of any algorithm for multiplying 3× 3 matrices having bilinear complexity l≤ 23 is isomorphic to a subgroup of the product Sₗ× S₃ of the symmetric groups Sₗ and S₃ .
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V. P. Burichenko (2026) studied this question.
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