## Question

###### D. Let F and Fz be distinct reflections in dihedral group Dnpoint ) Show that FiFz # Ro_ points) If FiFz = FFi, show that FFz = Risg_points) Prove that an Abelian group with two elements of order 2 must have subgroup of orderpoints) Find all subgroups and determine the subgroup lattice of Zaz 3 points) Suppose G is group and a,b â‚¬ G. Suppose that the order of is odd, and aba-! =6-1 Show that b2

D. Let F and Fz be distinct reflections in dihedral group Dn point ) Show that FiFz # Ro_ points) If FiFz = FFi, show that FFz = Risg_ points) Prove that an Abelian group with two elements of order 2 must have subgroup of order points) Find all subgroups and determine the subgroup lattice of Zaz 3 points) Suppose G is group and a,b â‚¬ G. Suppose that the order of is odd, and aba-! =6-1 Show that b2

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