Abstract
A monoid M that admits a finite convergent presentation satisfies the homological finiteness condition FP∞ and Squier's combinatorial property of having finite derivation type. Although Squier has given an example of a finitely presented monoid S 1 that satisfies the condition FP∞, but that does not have finite derivation type, the exact relationship between these two conditions is unsolved. Here we establish a partial result by showing that for finitely presented monoids the property of having finite derivation type implies the homological finiteness conditions FP 3 . Hence, the property FP 3 is strictly weaker than the property of having finite derivation type.
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