论文标题
有限古典群体中的中心化和共轭课
Centralizers and conjugacy classes in finite classical groups
论文作者
论文摘要
令$ \ mathscr {c} $为在有限字段上定义的经典组。我们向以下密切相关的问题提供了全面的理论解决方案：1）列出$ \ Mathscr {C} $的每个共轭类别的代表。 2）给定$ x \ in \ mathscr {c} $，描述centralizer $ c _ {\ mathscr {c}}}（x）$ in $ x $ in $ \ mathscr {c} $，通过提供其组结构和生成集。 3）给定$ x，y \ in \ mathscr {c} $，确定$ x $和$ y $是否在$ \ mathscr {c} $中是偶联的，如果它们是$ \ mathscr {c} $，并且，如果它们是$ z \ in \ mathscr {c} $ in \ mathscr {c} $，以免$ z^{ - 1} xz xz xz = y $。我们还制定了实用算法来解决这些问题，并已在岩浆中实施了这些问题。
Let $\mathscr{C}$ be a classical group defined over a finite field. We present comprehensive theoretical solutions to the following closely related problems: 1) List a representative for each conjugacy class of $\mathscr{C}$. 2) Given $x \in \mathscr{C}$, describe the centralizer $C_{\mathscr{C}}(x)$ of $x$ in $\mathscr{C}$, by giving its group structure and a generating set. 3) Given $x,y \in \mathscr{C}$, establish whether $x$ and $y$ are conjugate in $\mathscr{C}$ and, if they are, find explicit $z \in \mathscr{C}$ such that $z^{-1}xz = y$. We also formulate practical algorithms to solve these problems and have implemented them in Magma.
