Recent content by aliciaislol

so I did that and I came up with: 0+<3> = {0,3,6,9,12,15} 1+<3> = {1,4,7,10,13,16} 2+<3> = {2,5,8,11,14,17} 3+<3> = {3,6,9,12,15,0} 4+<3> = {4.7.10.13.16.1} 5+<3> = {5,8,11,14,17,2} So I get that 0 & 3 are tha same, 1&4 are the same and 2&5 are the same. So I have to do n(5+<3>)=...

Thank you, I figured out where it went wrong it was an nth root not power. Thnx again:smile:

Homework Statement Show that II18 / <3> is isomorphic to II3. Homework Equations II18 = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18} <3> = {0,3,6,9,12,15} II3 = {1,2,3} II18 / <3> = {3,6,9,12,15,18} The Attempt at a Solution

Homework Statement Find the order of the element 5 + <3> in the quotient group II18/ <3>. Homework Equations II18 = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18} <3> = {3,6,9,12,15,18} 5 + <3> = {5,8,11,14,17,2} order is the number of elements The Attempt at a Solution I am...

Homework Statement Consider III2, the additive group of integers modulo 12, and let f : II12 -->II12 be defined by f(x) = 3x. Find imf. Homework Equations II12 = {1,2,3,4,5,6,7,8,9,10,11,12} II12 / ker f is isomorphic to image of f The Attempt at a Solution I don't know were to...

Homework Statement Consider C^x, the multiplicative group of nonzero complex numbers, and let f:C^x --> C^x be defined by f(x)=x^4. Find ker f. Homework Equations C - complex numbers e^i2xpi = cos theta + isin theta element oof C R - reals Z- integers where R/Z This is the equation...