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Element structure of dihedral group:D8

2 bytes added, 16:45, 28 March 2012
Interpretation as unitriangular matrix group
| non-identity element, but central (has Jordan blocks of size one and two respectively) || <math>(x - 1)^2</math> || 1 || 1 || <math>q - 1</math> || 1 || <math>q - 1</math> || 1 || <math>\{ a^2 \}</math> || <math>p</math> || 2 || <math>a_{12} = a_{23} = 0</math> <math>a_{13} \ne 0</math>
|-
| non-central, has Jordan blocks of size one and two respectively || <math>(x - 1)^2</math> || <math>q</math> || 2 || <math>2q 2(q - 21)</math> || 2 || <math>2q(q - 1)</math> || 4 || <math>\{ x, a^2x, \}, \{ ax, a^3x \}</math> || <math>p</math> || 2 || <math>a_{12}a_{23} = 0</math>, but not both <math>a_{12}</math> and <math>a_{23}</math> are zero
|-
| non-central, has Jordan block of size three || <math>(x - 1)^3</math> || <math>q</math> || 2 || <math>(q - 1)^2</math> || 1 ||<math>q(q - 1)^2</math> || 2 || <math>\{ a, a^3 \}</math> || <math>p</math> if <math>p</math> odd<br>4 if <math>p = 2</math> || 4 || both <math>a_{12}</math> and <math>a_{23}</math> are nonzero
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