In this paper, we study properties and constructions of a general family of involutions of finite abelian groups, especially those of finite fields. The involutions we are interested in have the form \(\lambda +g\circ \tau \), where \(\lambda \) and \(\tau \) are endomorphisms of a finite abelian group and g is an arbitrary map on this group. We present some involutions explicitly written as polynomials for the special cases of multiplicative and additive groups of finite fields.

中文翻译：

---

有限域上显式构造的有限阿贝尔群的对合

在本文中，我们研究有限交换群（特别是有限域）的一般对合族的性质和构造。我们感兴趣的对合具有\(\lambda +g\circ \tau \) 的形式，其中\(\lambda \)和\(\tau \)是有限阿贝尔群的自同态， g是上的任意映射这个组。对于有限域乘法和加法群的特殊情况，我们提出了一些明确写为多项式的对合。