I'd like to know whether it is possible to find a characterization (cardinality?) of the set of finite, non-abelian groups generated by two elements $a$ and $b$ whose order is $3$? Is it the same task than finding all possible relations between $a$ and $b$ (for instance $aabba=bab$)? Thanks by advance for any comment
2026-04-06 12:24:34.1775478274
groups generated by two elements of order 3
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Maybe interesting to know, this touches the famous Burnside problem, posed by William Burnside in 1902 and one of the oldest and most influential questions in group theory. It asks whether a finitely generated group in which every element has finite order must necessarily be finite.