- #1
davidbenari
- 466
- 18
Homework Statement
Find a direct product representation for the quaternion group. Which are your options?
Homework Equations
The Attempt at a Solution
Theorem: The internal direct product of normal subgroups forms a homomorphism of the group.
https://proofwiki.org/wiki/Internal_Group_Direct_Product_of_Normal_Subgroups
The quaternion group as 6 normal subgroups, 4 of which are proper.
Let's suppose I only choose proper subgroups. The orders of these are 2,4,4,4.
Then I can form the product (grouporder2)x(anyothergrouporder4) and assure myself that it is a isomorphism.
Therefore, I've created a direct product representation.
Is this correct?