Abstract Algebra: practice problems 9-13-16, chapter 4 Gallian

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here we study a generator problem in infinite cyclic case, a particular cyclic group question, then we play with the problem of finding the order of elements in the Dihedral groups, eventually we give an induction argument to show all rotation-reflection elements have order 2.
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I knew group theory was addictive but I'm literally glued to my seat and notebook, for days now, watching these awesome lectures and reading Gallian. Thanks for the generosity of uploading these videos sir 🙏

NaderHGhanbari