Group Structure, Order of two groups - I have questions about constructing a group structure, how to identify the order of a paired group when they have different orders and method of figuring out the group identity and the inverse of a pa ...
2 Problems - 6. Let (G, *) be a group. Show that each equation of either the form ax = b or the form xa = b has a unique solution in G.
7. Show that (R - {1}, *), where a * b = a + b + ab is a group
group proofs - Let G be a group. x and y are elements of G. Prove that:
a. The inverse of xy is y^-1x^-1
b. The identity element, e, is unique
c. The inverse of any element x of G is unique
d. If xy = xz ...