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3. Let Gl₂(F) be the group of invertible 2 × 2 matrices over the finite field Fa of q elements, where q is an odd prime
Posted: Mon Jul 11, 2022 12:45 pm
by answerhappygod
- 3 Let Gl F Be The Group Of Invertible 2 2 Matrices Over The Finite Field Fa Of Q Elements Where Q Is An Odd Prime 1 (88.25 KiB) Viewed 29 times
3. Let Gl₂(F) be the group of invertible 2 × 2 matrices over the finite field Fa of q elements, where q is an odd prime power. Let Sl₂(F₁) = ker(det) be the subgroup containing those which have determinant 1. Let PGl2(Få) be the quotient of Gl₂(F) by the scalar matrices {\I | \ € FX}. Find the orders of these three groups. Are Sl₂(F) and PGl2(F₁) isomorphic?