In the present paper we show that it is possible to obtain the well known Pauli group P = 〈X,Y,Z | X² = Y² = Z² = 1,(Y Z)⁴ = (ZX)⁴ = (XY )⁴ = 1〉 of order 16 as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere S³. The first of these spaces of orbits is realized via an action of the quaternion group Q₈ on S³; the second one via an action of the cyclic group of order four \(\mathbb {Z}(4)\) on S³. We deduce a result of decomposition of P of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.

在本文中，我们表明有可能获得众所周知的泡利族P = 〈X，Y，Z |。X ² = Y ² = Z ² = 1，（Y Z）⁴ =（Z X）⁴ =（X Y）⁴ = 1〉作为16维3维球面轨道的两个不同空间的适当商群。S ³。第一轨道的这些空间的通过四元组的动作实现Q ₈上S ³ ; 第二个是通过S ³上四阶\（\ mathbb {Z}（4）\）的循环群的作用来实现的。我们推导了具有拓扑性质的P分解的结果，然后结合伪费米子理论，找到了对该分解的可能的物理解释。