My book defines a generator a of a cyclic group as:
Almost immediately after, it gives an example with , and the generator <2>. but it says...
Where are those numbers (0, 2, 4, ..., 16) coming from? If I follow the definition of a generator exactly,
And obviously,
What?
Grr, I keep typing responses and the forum erases them when I hit reply...??
Anyways,
So how do I know it's addition? Is it just standard and assumed that with , addition is always used for cyclic groups? What about Q, C, R, etc?
So when it's addition, the definition of a generator changes from
to
?
as other have pointed out in other threads, a set is not a group, so a multiplication must be specified.Grr, I keep typing responses and the forum erases them when I hit reply...??
Anyways,
So how do I know it's addition? Is it just standard and assumed that with , addition is always used for cyclic groups? What about Q, C, R, etc?
however, with , it is usually obvious from context that addition modulo n is intended, since has no multiplicative inverse. this applies to the other sets you mentioned as well.