Abstract Algebra: Theory and Applications · Problem 9.4.9

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · group-isomorphism

Problem

Let

G = \mathbb{R} \setminus \{-1\}

and define a binary operation on

G

a * b = a + b + ab.

Prove that

G

is a group under this operation. Show that

(G, *)

is isomorphic to the multiplicative group of nonzero real numbers.