ISOMORPHISM

Consider these multiplication tables.

1. Are they all tables of abelian groups?

2. Which of these (if any) are isomorphic? WHY?

3. Can you determine the order of each element?

	e1	a	b	c		e2	x	y	z
e1	e1	a	b	c	e2	e2	x	y	z
a	a	e1	c	b	x	x	y	z	e2
b	b	c	e1	a	y	y	z	e2	x
c	c	b	a	e1	z	z	e2	x	y

	1	-1	i	-i		0	1	2	3
1	1	-1	i	-i	0	0	1	2	3
-1	-1	1	-i	i	1	1	2	3	0
i	i	-i	-1	1	2	2	3	0	1
-i	-i	i	1	-1	3	3	0	1	2