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
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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) (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.
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