Pauli group

In physics and mathematics, the Pauli group formula_1 on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix formula_2 and all of the Pauli matrices
together with the products of these matrices with the factors formula_4 and formula_5:
The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli.
The Pauli group on formula_7 qubits, formula_8, is the group generated by the operators described above applied to each of formula_7 qubits in the tensor product Hilbert space formula_10.
As an abstract group, formula_11 is the central product of a cyclic group of order 4 and the dihedral group of order 8.
The Pauli group is a representation of the gamma group in three-dimensional Euclidean space. It is "not" isomorphic to the gamma group; it is less free, in that it's chiral element is formula_12 whereas there is no such relationship for the gamma group.