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

Vaughan-Lee, Michael

doi:10.22108/ijgt.2020.123980.1638

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

Document Type : Research Paper

Author

Michael Vaughan-Lee

Oxford University Mathematical Institute, United Kingdom

10.22108/ijgt.2020.123980.1638

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 $25$.

Keywords

20.1001.1.22517650.2021.10.4.2.7

Main Subjects

20D15 Nilpotent groups, p-groups

References

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