Schur's exponent conjecture - counterexamples of exponent $5$ and exponent $9$

Document Type : Research Paper

Author

Oxford University Mathematical Institute, United Kingdom

Abstract

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 $25$.

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