论文标题
小组的模块化同构问题 - 重新审视Eick的算法
The Modular Isomorphism Problem for small groups -- revisiting Eick's algorithm
论文作者
论文摘要
我们研究了B. eick描述的算法的改进，研究小阶的组的模块化同构问题（MIP）。我们的进步允许确定$ i（kg）/i（kg）^m $的商品，而无需先计算完整的增强理想$ i（kg）$。它使我们能够验证MIP对订单$ 3^7 $的组有一个正面答案，并大大减少需要检查订单组$ 5^6 $的案例。我们进一步提供了观察Bagiński的证据，并为Bleher，Kimmerle，Roggenkamp和Wursthorn的问题提供了负面答案。
We study the Modular Isomorphism Problem (MIP) for groups of small order based on an improvement of an algorithm described by B. Eick. Our improvement allows to determine quotients $I(kG)/I(kG)^m$ of the augmentation ideal without first computing the full augmentation ideal $I(kG)$. It allows us to verify that the MIP has a positive answer for groups of order $3^7$ and to significantly reduce the cases that need to be checked for groups of order $5^6$. We further provide a proof for an observation of Bagiński and provide a negative answer to a question of Bleher, Kimmerle, Roggenkamp and Wursthorn.
