For Groups the Property of Having Finite Derivation Type is Equivalent to the Homological Finiteness Condition FP_3

@article{Cremanns1996ForGT,
  title={For Groups the Property of Having Finite Derivation Type is Equivalent to the Homological Finiteness Condition FP_3},
  author={Robert Cremanns and Friedrich Otto},
  journal={J. Symb. Comput.},
  year={1996},
  volume={22},
  pages={155-177}
}
The homological niteness property F P 3 and the combinatorial property of having nite derivation type both are necessary conditions for nitely presented monoids to admit a nite convergent presentation. For monoids in general, the property of having nite derivation type is strictly stronger than the property F P 3. Here we show that for groups these two properties are equivalent. The proof exploits a result of 6], which states that a group G, which is given through a nite presentation hX; Ri… CONTINUE READING

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