for the cyclic group of order 16 generated by a , show that a^4 generates an invariant subgroup
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for the cyclic group of order 16 generated by a , show that a^4 generates an invariant subgroup.
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- 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.Give an example of a cyclic group of smallest order that containsboth a subgroup isomorphic to Z12 and a subgroup isomorphic toZ20. No need to prove anything, but explain your reasoning.Give an example of the dihedral group of smallest order that contains a subgroup isomorphic to Z12 and a subgroup isomorphic to Z20. No need to prove anything, but explain your reasoning.
- I need help proving that subgroups and quotient groups of a solveable group are solveable for abstarxct algebraWrite under isomorphism all abelian and non-abelian groups of order 8 and their respective subgroups. Please be as clear as possible and legible. Thank you.Write under isomorphism all the abelian groups of order 8 and their respective subgroups. Please show all the steps as clear as possible expleining them. Thank you