## Some standard policies

• Homework is due at the beginning of class on the Wednesday after it is assigned. No late homework will be accepted.

• I encourage you to work in groups to solve the problems; your write-ups, however, should be completed individually.

• I will assign homework on a weekly basis; I expect clearly organized and worded solutions (if you are able and willing to type even better). I will consider anything illegible to be wrong.

## Assignments

• Homework 1: (Due September 5)
1.1: 9, 15, 25, 28, 29
1.2: 5
1.3: 1, 6, 15, 18
1.5: 1

• Homework 2: (Due September 12)
1.2: 7
1.4: 5, 11 (a), (b), (e)
1.6: 2, 3, 20, 23
1.7: 8, 14, 15, 18, 19

• Homework 3: (Due September 19)
2.1: 8, 9, 14
2.2: 6, 10, 12
2.3: 25
2.4: 3, 12, 15, 16
+ Show that a finite group with no more that two maximal subgroups is cyclic.

• Homework 4: (Due September 26)
2.5: 12, 13, 14
3.1: 11, 19, 22, 36, 41
3.2: 4, 9, 18
+ Suppose N is a nontrivial abelian subgroup of G, minimal with the property that it is normal in G. Let H be a proper subgroup of G such that NH=G. Show that the intersection of N with H is trivial and H is a maximal subgroup of G.

• Homework 5: (Due October 3)
3.3: 6, 7, 9, 10
3.4: 2, 7, 11
3.5: 6, 10
4.1: 7, 9

• Homework 6: (Due October 17)
4.2: 9, 11
4.3: 13, 19, 23, 24, 33
4.4: 3, 8 (b)-(c), 18, 20 (a)-(b)
+: Show that if a simple group has order less 60, then it is abelian (of prime order)

• Homework 7: (Due October 24)
4.5: 16, 26, 30, 32, 35, 44
4.6: 4
5.1: 4
5.4: 15, 19
5.5: 12, 18, 23

• Homework 8: (Due October 31)
5.2: 8, 14
6.1: 7, 10, 20, 24, 25, 26, 31
+: Without using Feit--Thompson, show that if the order of group is greater than 60 and less than or equal to 100, then it is only simple if it is abelian.

• Homework 9: (Due November 7)
6.2: 4, 5, 6, 7, 10, 12, 22, 25
6.3: 10, 12, 14

• Homework 10: (Due November 14)
7.1: 7, 11, 14
7.2: 2, 7, 13
7.3: 22, 25, 29, 34
7.4: 10, 30, 37

• Homework 11: (Due December 5)
7.5: 4, 5
7.6: 1, 6
8.1: 3, 7
8.2: 6, 7, 8
8.3: 2, 6, 11

• Homework 12: (Due December 12)
9.1: 4, 10, 13
9.2: 2, 3, 4, 10
9.3: 3
9.4: 7, 12, 16, 17