In this paper we extend some group-like concepts to generalized digroups. We exhibit examples of non-abelian cyclic generalized digroups. We show that abelian generalized digroups are tightly related to left commutative semigroups with left identities and right inverses, and characterize these semigroups using generalized digroups properties. We also present symmetric generalized digroups and the transformation generalized digroup.

中文翻译：

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Abelian和对称广义二群

在本文中，我们将一些类似类的概念扩展到广义二类。我们展示了非阿贝尔循环广义二群的例子。我们表明，阿贝尔广义二群与具有左恒等和右逆的左可交换半群紧密相关，并使用广义二群性质来表征这些半群。我们还提出了对称广义二群和变换广义二群。