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 writeups, 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 FeitThompson, 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