Thread: Isomorphic groups

Here is a set of four groups: Z4, Z2 x Z2, P2, V
Determine which groups are isomorphic to which others.

* P2 denotes the group of subsets of a two element set
* V denotes the group of the four complex numbers {i, -i, 1, -1} with respect to multiplication.

Thanks for the help!!

Originally Posted by jzellt

Here is a set of four groups: Z4, Z2 x Z2, P2, V
Determine which groups are isomorphic to which others.

* P2 denotes the group of subsets of a two element set
* V denotes the group of the four complex numbers {i, -i, 1, -1} with respect to multiplication.

Thanks for the help!!

How much group theory do you know? Since all groups of order four are abelian. Then, by the structure theorem any group of order four is isomorphic to or according to whether their is an element of order or not.

Originally Posted by jzellt

Here is a set of four groups: Z4, Z2 x Z2, P2, V
Determine which groups are isomorphic to which others.

* P2 denotes the group of subsets of a two element set
* V denotes the group of the four complex numbers {i, -i, 1, -1} with respect to multiplication.

Thanks for the help!!

Well, the first group is the cyclic one of order 4, and the second one is the Klein group (non-cyclic

of order 4), so what kind of groups of order 4 are the 3rd and 4th ones?

Tonio