We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define H[r, s, p], a family of Riordan arrays. We generalize conditions for involutions, and pseudo-involutions of H[r, s, p], and we present stabilizers of this family. We find abelian subgroups as intersections of Riordan subgroups and show some alternative semi-direct products of the Riordan group.

中文翻译：

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Riordan子群的代数性质

我们介绍了Riordan阵列的群结构的性质。我们检查了已知Riordan子组之间的相似属性，并由此定义了Riordan数组家族H [ r，  s，  p ]。我们归纳了H [ r，  s，  p ]的对合和拟对合的条件，并给出了该族的稳定子。我们发现阿贝尔子群是Riordan子群的交集，并展示了Riordan群的一些替代半直接乘积。