تقرير
The directed Cayley diameter and the Davenport constant
| العنوان: | The directed Cayley diameter and the Davenport constant |
|---|---|
| المؤلفون: | András, Réka, Cziszter, Kálmán, Domokos, Mátyás, Szöllősi, István |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Primary 20D60, Secondary 20M14, 20K01 |
| الوصف: | The directed Cayley diameter of a finite group is investigated in terms of the monoid of product-one sequences over the group, via the new notion of directed geodesic atoms. Two quantities associated to the set of directed geodesic atoms provide lower and upper bounds for the directed Cayley diameter. An algorithm for computing the directed geodesic atoms is implemented in GAP, and is applied to determine the above mentioned quantities for all non-abelian groups of order at most $42$, and for the alternating group of degree $5$. Furthermore, the small and large Davenport constants of all these groups are computed (excepting the large Davenport constant for $A_5$), extending thereby the formerly obtained results on the groups of order less than $32$. Along the way the directed Cayley diameter of a finite abelian group is expressed in terms of its invariants. Comment: v2: final table is extended with further data |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.04607 |
| رقم الأكسشن: | edsarx.2401.04607 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |