Abstract Algebra: practice problems 9-6-16, chapter 2 and 3 Gallian

here I work a subgroup test problem and I give the proof that frf=r^(-1) in the case Dn has even n. The proof I gave in Lecture held for odd n. I also answer a few random questions and show U(20) is not cyclic.

[acertainayush]

21:30 if we introduce 3rd-dimensional observer, we don't have to prove it for different types of dihedrals, just imagine watching the 2d polygon from the backside rotate it, come frontside and you see the inverse effect of that rotation if you'd have done it on frontside! => frf=r^-1

similarly; first rotate 2d polygon from frontside and then go backside then rotate again; come back to the front side, you'd see no effect! => rfr=1

[toposopher]

21:30 if we introduce 3rd-dimensional observer, we don't have to prove it for different types of dihedrals, just imagine watching the 2d polygon from the backside rotate it, come frontside and you see the inverse effect of that rotation if you'd have done it on frontside! => frf=r^-1

similarly; first rotate 2d polygon from frontside and then go backside then rotate again; come back to the front side, you'd see no effect! => rfr=1

[marshidden]

21:30 if we introduce 3rd-dimensional observer, we don't have to prove it for different types of dihedrals, just imagine watching the 2d polygon from the backside rotate it, come frontside and you see the inverse effect of that rotation if you'd have done it on frontside! => frf=r^-1

similarly; first rotate 2d polygon from frontside and then go backside then rotate again; come back to the front side, you'd see no effect! => rfr=1

[toposopher]

21:30 if we introduce 3rd-dimensional observer, we don't have to prove it for different types of dihedrals, just imagine watching the 2d polygon from the backside rotate it, come frontside and you see the inverse effect of that rotation if you'd have done it on frontside! => frf=r^-1

similarly; first rotate 2d polygon from frontside and then go backside then rotate again; come back to the front side, you'd see no effect! => rfr=1