# SOLUTIONS OF SOME HOMEWORK PROBLEMS Problem set 1

**SOLUTIONS** OF SOME **HOMEWORK** PROBLEMS **MATH** 114 Problem set 1 4. Let D4 denote the group of symmetries of a square. Find the order of D4 and list all normal **subgroups** in D4. Solution. D4 has 8 elements: 1,r,r2,r3, d 1,d2,b1,b2, where r is the rotation on 90 , d 1,d2 are ﬂips about diagonals, b1,b2 are ﬂips about the lines joining the centersof opposite sides of a square.

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