Recall the dihedral group D = (o,p: p = = e.op=po). Show that if n...

 

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Recall the dihedral group D₁ = (o,p: p² = ² = e.op=p¹o). Show that if n is even then D, has normal subgroup of order 2 (note order, not index. You may find the fact that op = p o useful.) Recall the dihedral group D₁ = (o,p: p² = ² = e.op=p¹o). Show that if n is even then D, has normal subgroup of order 2 (note order, not index. You may find the fact that op = p o useful.) Recall the dihedral group D₁ = (o,p: p² = ² = e.op=p¹o). Show that if n is even then D, has normal subgroup of order 2 (note order, not index. You may find the fact that op = p o useful.) Recall the dihedral group D₁ = (o,p: p² = ² = e.op=p¹o). Show that if n is even then D, has normal subgroup of order 2 (note order, not index. You may find the fact that op = p o useful.)

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ANSWER To show that D has a normal subgroup of order 2 when n is even we will construct such a subgr... View the full answer