Find all abelian groups (upto isomorphism) of order 3375.
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Find all abelian groups (upto isomorphism) of order 3375.
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- Find two groups of order 6 that are not isomorphic.Exercise 8 states that every subgroup of an abelian group is normal. Give an example of a nonabelian group for which every subgroup is normal. Exercise 8: Show that every subgroup of an abelian group is normal.Show that every subgroup of an abelian group is normal.
- Find all homomorphic images of the quaternion group.12. Find all normal subgroups of the quaternion group.10. Prove that in Theorem , the solutions to the equations and are actually unique. Theorem 3.5: Equivalent Conditions for a Group Let be a nonempty set that is closed under an associative binary operation called multiplication. Then is a group if and only if the equations and have solutions and in for all choices of and in .