论文标题
本地有限的简单组中有限群体的中心者
Centralisers of finite groups in locally finite simple groups
论文作者
论文摘要
我们在负面的问题中回答了哈特利关于有限群体的表示的问题，该问题是通过构建有限的简单群体的示例，这些示例具有任意较大的表示，其内态戒指仅包含标量。结果，我们表明有有限的简单群体属于本地有限的简单组$ sl（\ infty，\ mathbb {f} _q）$ at Trivial Centraliser。我们最小的示例是$ a_6 $，$ q = 9 $。
We answer in the negative a question of Hartley about representations of finite groups, by constructing examples of finite simple groups with arbitrarily large representations whose endomorphism ring consists of just the scalars. We show as a consequence that there are finite simple groups of automorphisms of the locally finite simple group $SL(\infty,\mathbb{F}_q)$ with trivial centraliser. The smallest of our examples is $A_6$ with $q=9$.
