Show that the groups Z8xZ20xZ12 and Z120xZ4xZ4 are isomorphic by define a one-one and onto map? what are the generators of these groups? Thanks
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- Write 20 as the direct sum of two of its nontrivial subgroups.15. Prove that on a given collection of groups, the relation of being a homomorphic image has the reflexive property.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 .
- 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.Find all homomorphic images of the quaternion group.