2-Sylow subgroup of special linear group:SL(2,5)

From Groupprops
Revision as of 13:49, 28 June 2011 by Vipul (talk | contribs) (Created page with "{{particular subgroup| subgroup = quaternion group| group = special linear group:SL(2,5)}} <math>G</math> is the special linear group:SL(2,5), i.e., the [[special linear gro...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) quaternion group and the group is (up to isomorphism) special linear group:SL(2,5) (see subgroup structure of special linear group:SL(2,5)).
VIEW: Group-subgroup pairs with the same subgroup part | Group-subgroup pairs with the same group part | All pages on particular subgroups in groups

G is the special linear group:SL(2,5), i.e., the special linear group of degree two over field:F5. In other words, it is the group of invertible 2 \times 2 matrices of determinant 1 over the field with three elements. The field has elements 0,1,2,3,4 with 4 = -1.

H is the subgroup:

\{ \begin{pmatrix} 1 & 0 \\ 0 & 1 \\\end{pmatrix}, \begin{pmatrix} 4 & 0 \\ 0 & 4 \\\end{pmatrix}, \begin{pmatrix} 0 & 4 \\ 1 & 0 \\\end{pmatrix}, \begin{pmatrix} 0 & 1 \\ 4 & 0 \\\end{pmatrix}, \begin{pmatrix} 4 & 4 \\ 4 & 1 \\\end{pmatrix}, \begin{pmatrix} 1 & 1 \\ 1 & 4 \\\end{pmatrix}, \begin{pmatrix} 1 & 4 \\ 4 & 4 \\\end{pmatrix}, \begin{pmatrix} 4 & 1 \\ 1 & 1 \\\end{pmatrix} \}