Prove that every subgroup of the quaternion group Q8 is normal. Deter- mine all the quotient groups.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 8E: Show that every subgroup of an abelian group is normal.
Question

Prove that every subgroup of the quaternion group Q8 is normal. Deter- mine all the quotient groups.

Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer