There is a long-standing conjecture attributed to I. Schur that if $G$ is a finite group with Schur multiplier $M(G)$ then the exponent of $M(G)$ divides the exponent of $G$. In this note I give an example of a four generator group $G$ of order $5^{4122}$ with exponent $5$, where the Schur multiplier $M(G)$ has exponent $25$.
Vaughan-Lee, M. (2021). Schur's exponent conjecture - counterexamples of exponent $5$ and exponent $9$. International Journal of Group Theory, 10(4), 167-173. doi: 10.22108/ijgt.2020.123980.1638
MLA
Michael Vaughan-Lee. "Schur's exponent conjecture - counterexamples of exponent $5$ and exponent $9$". International Journal of Group Theory, 10, 4, 2021, 167-173. doi: 10.22108/ijgt.2020.123980.1638
HARVARD
Vaughan-Lee, M. (2021). 'Schur's exponent conjecture - counterexamples of exponent $5$ and exponent $9$', International Journal of Group Theory, 10(4), pp. 167-173. doi: 10.22108/ijgt.2020.123980.1638
VANCOUVER
Vaughan-Lee, M. Schur's exponent conjecture - counterexamples of exponent $5$ and exponent $9$. International Journal of Group Theory, 2021; 10(4): 167-173. doi: 10.22108/ijgt.2020.123980.1638
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