64 740
Assignments Done
99,3%
Successfully Done
In September 2018

Answer to Question #23892 in Abstract Algebra for jeremy

Question #23892
Let k be any field of characteristic 3, G = S3 and let V be the kG-module ke1 ⊕ ke2 ⊕ ke3/k(e1 + e2 + e3),
on which G acts by permuting the ei’s. Show that this realizes G as a linear group in GL(V ).
Expert's answer
Since (123) does not act triviallyon V , the representation homomorphism ϕ : G → GL(V ) must be injective.Therefore, ϕrealizes G as alinear group in GL(V).

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions