Question

What are all the cosets of \(Z_4\) of \(Z_2\)?

Answer 1

or would that be better notated as 4Z of 2Z ?

Answer 2

i think the first one

Answer 3

cosets of 4Z of Z

4Z = {...,-8,-4,0,4,8,...}

1+4Z = {...,-7,-3,1,5,9,...}

2+4Z = {...,-6,-2,2,6,10,...}

3+4Z = {...,-5,-1,3,7,11,...}

Answer 4

\(\mathbb{Z}_4=\{0,1,2,3\}\) which has only one non - trivial subgroup \(\{0,2\}\)

Answer 5

so i am thinking you want the cosets of \(\{0,2\}\) maybe

Answer 6

i have the hardest time trying to decipher what the end of chapter problems are actually asking for :)

Answer 7

i noticed something a few minutes ago with respect to permutations and mod n

Answer 8

if it says exactly what you wrote, i am pretty sure it means what i wrote
since \(\{0,2\}\) with addition mod 4 is the same as \(\{0,1\}\) with addition mod 2, i bet it is asking for the cosets of that

Answer 9

ill delve further into it tonight ... to see if ive got some misinformation seeping about me noggin

Answer 10

k
have fun

Answer 11

http://faculty.clayton.edu/Portals/455/Content/MATH3110-SP13/HW/M3110SP13-HW09-SOL.pdf

this seems to be it ....

Answer 12

i sense the {0,2} in that

Answer 13

lol well then i was wrong , wasn't i? it was the second thing you wrote

Answer 14

i spose i could interpret: find all cosets of nZ of kZ

list nZ, then add on the elements of kZ

keep the uniques sets

Answer 15

yeah pretty clear that in your case there will be only two right? the set of integers divisible by 4, and the set of integers divisible by 2 but not by 4

Answer 16

yep