This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 3124 Tuesday, November 1 Second Test. Answer All Problems. Please Give Explanations For Your Answers. 1. In Z 24 , prove that [ 4 ] , [ 6 ] = [ 10 ] . (10 points) 2. The following is part of the Cayley table for a group. Complete the table. a b c d a b b c b d (i.e. given a 2 = cd = b .) (10 points) 3. Let G be a group of order 25 and let A , B be subgroups of G with  A  =  B  . Prove that either A = B or A B = { e } . (10 points) 4. Let G be a cyclic group of order 72 and let H be a subgroup of order 2. Determine the number of subgroups of G containing H (including G and H ). 5. Prove that S 5 S 4 Z 5 . (10 points) 6. Let G = Z 12 and let H = [ 3 ] . (a) Write down the right cosets of H in G . (b) Construct the Cayley table for G / H . (10 points) Math 3124 Tuesday, November 1 Second Test Solutions 1. Since [ 10 ] = [ 4 ] [ 6 ] we see that [ 10 ] [ 4 ] , [ 6 ] . Now [ 4 ] = [ 10 ] [ 10 ] and [ 6 ] = [ 10 ] [ 10 ] [ 10 ] and we deduce that [ 4 ] , [...
View
Full
Document
 Fall '08
 PARRY
 Math, Algebra

Click to edit the document details