当前位置: X-MOL 学术J. Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
2-Blocks whose defect group is homocyclic and whose inertial quotient contains a Singer cycle
Journal of Algebra ( IF 0.8 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.jalgebra.2020.06.029
Elliot McKernon

We consider $2$-blocks of finite groups with defect group $D=Q \times R$ and inertial quotient $\mathbb{E}$ where $Q \cong (C_{2^m})^n$, $R \cong C_{2^r}$, and $\mathbb{E}$ contains a Singer cycle of $\operatorname{Aut}(Q)$ (an element of order $2^n-1$). We classify such blocks up to Morita equivalence when either $\mathbb{E}$ is cyclic or $r=1$. We achieve a partial classification when $r>1$ and $E$ is non-cyclic.

中文翻译:

2-缺陷群为同环且惯性商包含辛格圈的块

我们考虑具有缺陷群 $D=Q \times R$ 和惯性商 $\mathbb{E}$ 其中 $Q \cong (C_{2^m})^n$, $R \ cong C_{2^r}$,$\mathbb{E}$ 包含$\operatorname{Aut}(Q)$($2^n-1$阶元素)的Singer循环。当 $\mathbb{E}$ 是循环的或 $r=1$ 时,我们将这些块分类为 Morita 等价。当 $r>1$ 且 $E$ 是非循环时,我们实现了部分分类。
更新日期:2020-12-01
down
wechat
bug