论文标题
相对亚组的相对中心体
Relative centralisers of relative subgroups
论文作者
论文摘要
令$ r $为1，$ g = gl（n，r）$是$ n \ ge 3 $上的一般线性群体。在本文中，我们计算相对基本亚组的相对中心者或主要的一致性子组，对应于理想的$ a \ linlhd r $ modulo相对基本亚组或主要的一致性子组，对应于另一个理想的$ b \ lindrhd r $。 Modulo一致性子组在线性代数中基本上很容易练习。但是Modulo的基本子组非常棘手，我们只能通过交换戒指获得确定的答案，或者在某些情况下，只能通过Dedekind Rings获得。我们还讨论了一些进一步的相关问题，例如各种出生的换向子亚组等的相互关系，并提出了几个未解决的问题。
Let $R$ be an associative ring with 1, $G=GL(n, R)$ be the general linear group of degree $n\ge 3$ over $R$. In this paper we calculate the relative centralisers of the relative elementary subgroups or the principal congruence subgroups, corresponding to an ideal $A\unlhd R$ modulo the relative elementary subgroups or the principal congruence subgroups, corresponding to another ideal $B\unlhd R$. Modulo congruence subgroups the results are essentially easy exercises in linear algebra. But modulo the elementary subgroups they turned out to be quite tricky, and we could get definitive answers only over commutative rings, or, in some cases, only over Dedekind rings. We discuss also some further related problems, such as the interrelations of various birelative commutator subgroups, etc., and state several unsolved questions.
