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English
Pauli group
the 16-element group generated by the Pauli matrices
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Statements
instance of
finite group
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defining formula
{
±
1
,
±
i
,
±
σ
1
,
±
i
σ
1
,
±
σ
2
,
±
i
σ
2
±
σ
3
,
±
i
σ
3
}
≅
(
Z
4
×
Z
2
)
⋊
Z
2
{\displaystyle \{\pm 1,\pm \mathrm {i} ,\pm \sigma _{1},\pm \mathrm {i} \sigma _{1},\pm \sigma _{2},\pm \mathrm {i} \sigma _{2}\pm \sigma _{3},\pm \mathrm {i} \sigma _{3}\}\cong (Z_{4}\times Z_{2})\rtimes Z_{2}}
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in defining formula
i
{\displaystyle \mathrm {i} }
symbol represents
imaginary unit
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σ
i
{\displaystyle \sigma _{i}}
symbol represents
Pauli matrices
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Z
2
{\displaystyle Z_{2}}
symbol represents
Z2
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Z
4
{\displaystyle Z_{4}}
symbol represents
finite cyclic group
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1
{\displaystyle 1}
symbol represents
identity matrix
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group cardinality
16
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maintained by WikiProject
WikiProject Mathematics
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Identifiers
Freebase ID
/m/0d0b0f
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Microsoft Academic ID
2781040351
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ScienceDirect topic ID
mathematics/pauli-group
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enwiki
Pauli group
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