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You can do quick computations with http://servus.math.su.se/bergman/demo.html (The page deals with homogeneous relations, but you can add a new variable $t$, homogenise the relations you want using it, and the add relations saying that $t$ commutes with $a$, $b$ and $c$. Doing this with your relations gives what seems to be infinitely many elements in the (lexicographic) Groebner basis) |
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You can do quick computations with http://servus.math.su.se/bergman/demo.html (The page deals with homogeneous relations, but you can add a new variable $t$, homogenise the relations you want using it, and the add relations saying that $t$ commutes with $a$, $b$ and $c$. Doing this with your relations gives what seems to be infinitely many elements in the Groebner basis) |
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