Recent content by chibulls59

Since Aut(Z_p) is the set of maps that maps K-->K, wouldn't that mean that |Aut(Z_p)|=p?

Homework Statement Let G be a finite group and K a normal subgroup of G If |K|=p where p is a prime Prove that |G/CG(K)| divides p-1 Homework Equations The Attempt at a Solution I must show that |G| / |CG(K)| * something = p-1 I figured a good place to start would be to...

Homework Statement Let G be a group and K be a normal subgroup of G. Let x be an element of G Define Ax: K-->K given by Ax(k)=xkx-1 Prove that B: G-->Aut(K) given by B(x)=Ax is a well defined group homomorphism Homework Equations The Attempt at a Solution I found...

Oh I got it, for some reason I thought 9 was a prime number.

Homework Statement If A=<x> is a cyclic group of order 9 and B=<y> is a cyclic group of order 7. Deduce that Aut(A) is isomorphic to Aut(B) Homework Equations The Attempt at a Solution I already proved that Aut(A) and Aut(B) are cyclic but I don't understand how they can be...

Homework Statement Suppose that J is an ideal of R, and consider the ring R/J = {r + J | r 2 R}. Prove that X is an ideal of R/J is and only if there is an ideal I of R containing J such that J c I c R. Homework Equations The Attempt at a Solution

Suppose K= < x > is a cyclic group with 2 elements and H= S3 is symmetric group with 6 elements. Find all different cyclic subgroups of G= H x K. Now since K is generated by x with 2 elements, I have K= {1,x} and H= {1, (12), (13), (23), (123), (132)} What I am confused about is finding...