Answer to Question #18104 in Abstract Algebra for sanches

Question #18104

Assume char k = 2. Let A be an abelian 2'-group and let G be the semidirect product of A and a cyclic group <x> of order 2, where x acts on A by a → a^−1. If |A| < ∞, show that rad kG = k (Sum over g∈G)•g, and (rad kG)^2 = 0.

Expert's answer

Answer in progress...

Learn more about our help with Assignments: Abstract Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Assume char(k) = 3, and let G = S3. Determine the index of nilpotency for J, and find a k-basis for
2. char(k) = 3, and let G = S3. Compute the Jacobson radical J = rad(kG), and the factor ring kG/J.
3. Let k be a commutative ring and G be any group. If kG is left artinian, show that kG is right artini
4. Let k be a commutative ring and G be any group. If kG is left noetherian, show that kG is right noet
5. Let A be a normal elementary p-subgroup of a finite group G such that the index of the centralizer C
6. Let R be a commutative domain that is not a field. Show that not always R is not J-semisimple implie
7. Let R be a commutative domain that is not a field. Show that if R is not J-semisimple then R is semi