一句话：证明群元素均中心的幺半群簇 ZG 是局部的，并将其语言刻画为单例语言与正则交换语言的不交混洗的有限并。
本文研究幺半群簇 ZG，即所有属于群的元素都与其余元素交换（中心）的幺半群类。作者关心该簇的“局部性”，探究以确定半群作半直积后是否等于局部幺半群都落在 ZG 中的半群簇 LZG。证明上借助 Straubing 延迟定理，并考察幂等元范畴中的路径。主要结果为 ZG * D = LZG，从而证明 ZG 是局部的。文中还得到代数刻画 ZG = MNil ∨ Com，并精确刻画 ZG 语言：它们恰为单例语言与正则交换语言的不交混洗的有限并。
We study the variety ZG of monoids where the elements that belong to a group are central, i.e., commute with all other elements. We show that ZG is local, that is, the semidirect product ZG * D of ZG by definite semigroups is equal to LZG, the variety of semigroups where all local monoids are in ZG. Our main result is thus: ZG * D = LZG. We prove this result using Straubing's delay theorem, by considering paths in the category of idempotents. In the process, we obtain the characterization ZG = MNil \vee Com, and also characterize the ZG languages, i.e., the languages whose syntactic monoid is in ZG: they are precisely the languages that are finite unions of disjoint shuffles of singleton languages and regular commutative languages.