sol8 - Algebra , Assignment 8 Solutions 1. Three problems...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Algebra , Assignment 8 Solutions 1. Three problems about manipulating products of cyclic groups. (a) Write Z 2 Z 2 Z 2 Z 9 Z 5 Z 25 as the product of cyclic groups Z a i , 1 i s (you find the s ) with a i dividing a i +1 for all 1 i < s . Solution: We line up each power separately right justified: Z 2 Z 2 Z 2-- Z 9- Z 5 Z 25 Multiplying down the columns (note the numbers are relatively prime in the column so this can be done) gives the answer Z 2 Z 10 Z 450 . (b) Write Z 4 Z 40 Z 200 Z 1400 as the product of cyclic groups of prime power order. (Prime power includes primes themselves.) Solution: Break each up into its prime powers giving Z 4 Z 8 Z 5 Z 8 Z 25 Z 8 Z 25 Z 7 (c) Write Z 5 Z 6 Z 7 in both of the above forms. Solution: For the second we have Z 5 Z 2 Z 3 Z 7 . For the first each prime power appears only once so we have Z 210 . 2. Let G = Z 5 Z 25 Z 125 . Find the order of (3 , 10 , 12). Give a good description and a precise count on those ( a, b, c ) G order 25....
View Full Document

This note was uploaded on 04/01/2011 for the course MATH 101 taught by Professor Josephs during the Fall '08 term at NYU.

Page1 / 3

sol8 - Algebra , Assignment 8 Solutions 1. Three problems...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online