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clooneyisagenius

Member

Registered: 2007-03-25

Posts: 56

Subgroups of a Set // Abstract Algebra

Let Q be the group of rational numbers under addition and let Q* be the group of nonzero rational numbers under multiplication. In Q, list the elements in <1/2>. In Q*, list the elements in <1/2>. Find order of each element in Q and in Q*.

I know that....
for any element, a, from a group, G, we let <a> denote the set {a^n l n in Z}. I've finished other problems dealing with this but this problem is fooling me.

Thanks.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Subgroups of a Set // Abstract Algebra

In (ℚ,+), 0 has order 1; every other element has infinite order.
In (ℚ*,×), 1 has order 1 and −1 has order 2; every other element has infinite order.

Last edited by JaneFairfax (2007-09-13 11:57:22)

zorro

Guest

Re: Subgroups of a Set // Abstract Algebra

let Q and Q* be as in exercise 2. find the order of each element in Q and in Q*