(6) Define a binary operation ∗ on the set G = R^2 by (x, y) ∗...

(6) Define a binary operation ∗ on the set G = R^2 by (x, y) ∗ (x', y') = (x + x', y + y'e^x)

(a) Show that (G, ∗) is a group. Specifically, prove that the associative law holds, find the identity e, and find the inverse of (x, y) ∈ G.

(b) Show that the group G is not abelian.

(c). Show that the set H= (x*x=e) is a subgroup of G.

Solutions

Expert Solution

a. We proved G is a group

b. We shown G is not abelian

c. H is a trivial subgroup of G

Colby Messinger answered 1 year ago

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