论文标题
模块化同构问题和亚伯直接因素
The modular isomorphism problem and abelian direct factors
论文作者
论文摘要
让$ p $为素数，让$ g $为有限的$ p $ group。我们表明，最大的Abelian直接因子$ G $的同构类型，以及非阿布尔剩余直接因子的组代数的同构类型，由$ \ Mathbb f_p g $确定。为了做到这一点，我们解决了找到$ g $的特征子组的问题，使它们的相对增强理想仅取决于$ k $ kg $的$ k $ - 代数结构，其中$ k $是任何特征性$ p $的领域，并将其与模块化的同构问题联系起来，并依次reprov and reprov and reprov and retands sover。
Let $p$ be a prime and let $G$ be a finite $p$-group. We show that the isomorphism type of the maximal abelian direct factor of $G$, as well as the isomorphism type of the group algebra over $\mathbb F_p$ of the non-abelian remaining direct factor, are determined by $\mathbb F_p G$, generalizing the main result in arXiv:2110.10025 over the prime field. In order to do this, we address the problem of finding characteristic subgroups of $G$ such that their relative augmentation ideals depend only on the $k$-algebra structure of $kG$, where $k$ is any field of characteristic $p$, and relate it to the modular isomorphism problem, reproving and extending some known results.
