Fix g E G, where G is a group whose (original) operation we will suppress in the notation, for convenience. Define a new operation * on G this way: for any a, b e G, a * b = agb. Show that G with the...

Show that G with the operation * is a group. Fix g element of G, where G is a group whose (original) operation we will suppress in the notation, for convenience. Define a new operation * on G this way: for any a, b e G, a *b = agb.

Extracted text: Fix g E G, where G is a group whose (original) operation we will suppress in the notation, for convenience. Define a new operation * on G this way: for any a, b e G, a * b = agb. Show that G with the operation * is a group.