section 1.1 : 5, 7

section 1.2 : 1(f), 4(b), 6, 16, 19, 20, 24, 31, 32, 36

section 1.3 : 2, 6, 9, 11, 19, 21. You may also try problems in part C.

section 2.1 : 1, 5, 12, 21, 23, 31

section 2.2 : 6, 8, 9(b), 10(a)(d)

section 2.3 : 4, 7(a)(e), 13

section 7.1 : 2, 4(a)(b)(d), 8, 14, 18, 21, Show S_3=D_3.

section 7.2 : 4, 6, 9(a), 10, 16, 17, 18, 22, 25, 33, 36, Let p,q be two odd primes and (Z(2pq),+) is a group, show that there exist two elements, a and b, such that order of a+b is not the lcm of order of a and order of b.

section 7.3 : 1, 3, 7, 13, 17, 23, 24, 37, 41, 26 (i.e. show Z(G)= intersection of centraliers of all the elements in G.)

section 7.4 : 5, 7, 14, 19, 23, 24, 27, 28(b)(c), 44

section 3.1 : 4(b), 5(a)(b)(d), 6, 7, 10, 21, 23, 26, 31, 37

section 3.2 : 6, 9, 13, 15, 22, 28, 32, 34. Show that every nonzero element of Z_n is either a unit or a zero divisor.

section 3.3 : 1, 6, 7, 9, 11, 17, 21, 28, 32.

section 4.1 : 1(c)(d), 5(b), 7, 11, 12, 15, 16, 17

section 4.2 : 3, 4, 5a, 14

section 4.3 : 3(a), 5, 6, 9(c), 10, 12, 13, 15, 20, 22

section 4.4 : 2(c)(d), 3(c), 4(a), 5, 8(e), 10, 15, 18

section 4.5 : 1(d)(e), 3, 5(a)(c), 7, 8, 12, 19

section 5.1 : 1(a)(b), 3, 5, 8, 11, 12

section 6.1 : 1, 2, 10, 13, 14