تقرير
Schur's exponent conjecture -- counterexamples of exponent 5 and exponent 9
| العنوان: | Schur's exponent conjecture -- counterexamples of exponent 5 and exponent 9 |
|---|---|
| المؤلفون: | Vaughan-Lee, Michael |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, 20D15 |
| الوصف: | 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 $G$. It is easy to see that this conjecture holds for exponent 2 and exponent 3, but it has been known since 1974 that the conjecture fails for exponent 4. In this note I give an example of a group $G$ with exponent 5 with Schur multiplier $M(G)$ of exponent 25, and an example of a group $A$ of exponent 9 with Schur multiplier $M(A)$ of exponent 27. Comment: 8 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2008.06848 |
| رقم الأكسشن: | edsarx.2008.06848 |
| قاعدة البيانات: | arXiv |
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