Math 503
Practice for the test November 17, 2010
W. Heinzer
1. Let R be a commutative ring with 1 6= 0 and let P be an ideal of R.
(a) Define P is a prime ideal.
(b) If P is a prime ideal of R and I and J are ideals of R such that I J P , prove that I P
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Math 503
Practice for the test October 6, 2010
W. Heinzer
1. Let G be the group of rigid motions in R3 of a cube. What is the order of G? Justify your answer.
2. Prove or disprove that the dihedral group D24 is isomorphic to the symmetric group S4 .
3. Fo
Math 503
Practice for final 8:00 - 10:00 am Dec. 15, 2010
W. Heinzer
1. Determine the number of elements of order 3 in the symmetric group S4 .
2. Determine the number of elements of order 3 in the symmetric group S5 .
3. For the group A = Z2 Z4 = ha, b |