We find algebraic conditions on a group equivalent to the position of its equation solvability problem in the Chomsky Hierarchy. In particular, it is proved that a finitely generated group has a context-free equation solvability problem if and only if it is finite.

中文翻译：

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具有无上下文方程可解问题的组

我们在与Chomsky层次结构中的方程可解问题位置相等的组上找到代数条件。特别地，证明了，当且仅当它是有限的时，有限生成的组才具有上下文无关的方程可解性问题。