小于32阶群的Noether数和Davenport常数
The Noether numbers and the Davenport constants of the groups of order less than 32
摘要：
完成了小于32阶群Noether数的计算。结果表明，对于非模特征群，Noether数是在多重数自由表示上得到的，Noether数在子群和因子群上是严格单调的，且不依赖于特征.算法的开发和使用，以确定这些群体的大小达文波特常数。对于这些群体的Noether数是大于小达文波特常数，而第一个例子的一组的Noether数超过大达文波特常数被发现，部分回答了一个问题所提出的Geroldinger和Grynkiewicz。
英文摘要：
The computation of the Noether numbers of all groups of order less than thirty-two is completed. It turns out that for these groups in non-modular characteristic the Noether number is attained on a multiplicity free representation, it is strictly monotone on subgroups and factor groups, and it does not depend on the characteristic. Algorithms are developed and used to determine the small and large Davenport constants of these groups. For each of these groups the Noether number is greater than the small Davenport constant, whereas the first example of a group whose Noether number exceeds the large Davenport constant is found, answering partially a question posed by Geroldinger and Grynkiewicz.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
