Nilpotent multiplier of perfect group equals Schur multiplier

Statement

Suppose $G$ is a perfect group and $c$ is any nonnegative integer. Then, the class $c$-nilpotent multiplier of $G$ is isomorphic to the Schur multiplier of $G$.

Recall that, by definition, the Schur multiplier is the nilpotent multiplier for class $c=1$.

References

Journal references

• On the nilpotent multipliers of a group by John Burns and Graham Ellis, Math. Zeitschr., Volume 226, Page 405 - 428(Year 1997): ^{Official page (PDF downloadable)More info}, Proposition 2.11