SOLUTION: From Abstract Algebra class. Consider Z9 - { [ 0 ] } with respect to multiplication [ a ] [ b ] = [ ab ] modulo 9 . ( a ) Let G be the set of all [ a ] in Z9, - { [ 0 ] ) that

Algebra ->  Test -> SOLUTION: From Abstract Algebra class. Consider Z9 - { [ 0 ] } with respect to multiplication [ a ] [ b ] = [ ab ] modulo 9 . ( a ) Let G be the set of all [ a ] in Z9, - { [ 0 ] ) that      Log On


   

Question 1185787: From Abstract Algebra class.
Consider Z9 - { [ 0 ] } with respect to multiplication [ a ] [ b ] = [ ab ] modulo 9 .
( a ) Let G be the set of all [ a ] in Z9, - { [ 0 ] ) that have multiplicative inverses . Find G.
( b ) Prove that G is a group .
( c ) Prove or disprove : G is a cyclic group.
For this exercise I tried to find a generator but I couldn’t.
( d ) Find all distinct subgroups of G.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

In the Internet, I quickly found the source, which contains answers (with solutions) to most questions of your post.

To save my time, I will not reproduce it here; simply will give you the link

https://math.berkeley.edu/~kruckman/summer2013/final%20solutions.pdf

See problem (5) there.