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For a given group presentation of a group(finitely presented), I want to check whether it is residually solvable or not. Is there any good way to do it?

Actually, I'm curious whether the finitely presented group $G = < x_i, 1\leq i \leq m | w_i x_i w_i^{-1}w_i^{-1}x_{i+1}, 1\leq i \leq n-1 >$, where $w_i=x_j^{\pm 1}$ for some $j$.

2 added 169 characters in body

For a given group presentation of a group(finitely presented), I want to check whether it is residually solvable or not. Is there any good way to do it?

Actually, I'm curious whether the finitely presented group $G = < x_i, 1\leq i \leq m | w_i x_i w_i^{-1}, 1\leq i \leq n-1 >$, where $w_i=x_j^{\pm 1}$ for some $j$.

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# Is there any way to check whether a group is residually solvable?

For a given group presentation of a group(finitely presented), I want to check whether it is residually solvable or not. Is there any good way to do it?