Answer to Question #23732 in Abstract Algebra for john.george.milnor

Abstract Algebra

Question #23732

Show that for any prime p, a group G of order p2 must be abelian.

Expert's answer

Download Answer

Learn more about our help with Assignments: Abstract Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Show that, for any two groups G,H, there exists a (nonzero) ring R such that RG ∼ RH as rings.
2. For finite abelian groups G and H, show that RG ∼ RH as R-algebras iff |G| = |H| and |G/G2| = |H/H
3. Let G = [x] be a cyclic group of order 5. Show that a = 2x4 − x3 − 3x2 − x + 2is a unit of inf
4. Let G = [x] be a cyclic group of order 5. Show that U(ZG) = [u] × (±G) ∼ Z ⊕ Z2 ⊕ Z5.
5. Let G = [x] be a cyclic group of order 5. Show that u = 1− x2 − x3 is a unit of infinite order i
6. Let k be the algebraic closure of Fp and K = k(t), where t is an indeterminate. Let G be an elementa
7. Let Fk(G) be the k-space of class functions on G, given the inner product [μ, ν] = 1/|G| *(Sum ov