ahw4 - Math 4124 Wednesday February 16 Fourth Homework...

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Math 4124 Wednesday, February 16 Fourth Homework Solutions 1. 2.3.6 on page 60. In Z / 48 Z write out all elements of h a i for every a . Find all inclu- sions between subgroups in Z / 48 Z . Since 48 = 3 *16, 3 has two divisors and 16 has five divisors, we see that there are 2*5 = 10 subgroups. h 0 i = { 0 } Order 1 h 1 i = { 0 , 1 , 2 , . . . , 47 } order 48 h 2 i = { 0 , 2 , 4 , . . . , 46 } order 24 h 3 i = { 0 , 3 , 6 , . . . , 45 } order 16 h 4 i = { 0 , 4 , 8 , . . . , 44 } order 12 h 6 i = { 0 , 6 , 10 , . . . , 42 } order 8 h 8 i = { 0 , 8 , 12 , . . . , 40 } order 6 h 12 i = { 0 , 12 , 24 , 36 } order 4 h 16 i = { 0 , 16 , 32 } order 3 h 24 i = { 0 , 24 } order 2 Then we have h 1 i = h 5 i = h 7 i = h 11 i = h 13 i = h 17 i = h 19 i = h 23 i = h 25 i = h 29 i = h 31 i = h 35 i = h 37 i = h 41 i = h 43 i = h 47 i h 2 i = h 10 i = h 14 i = h 22 i = h 26 i = h 34 i = h 38 i = h 46 i h 3 i = h 9 i = h 15 i = h 21 i = h 27 i = h 33 i = h 39 i = h 45 i h 4 i = h 20 i = h 28 i = h 44 i h 6 i = h 18 i = h
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This note was uploaded on 01/02/2012 for the course MATH 4124 taught by Professor Staff during the Spring '08 term at Virginia Tech.

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ahw4 - Math 4124 Wednesday February 16 Fourth Homework...

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