Fall 2002
MT-A511 Graduate Algebra I
Homework Assignment 3

Due Wednesday October 23

Done individually

1. D & F: §4.5, # 23, p. 149
2. D & F: §4.5, # 32, p. 150
3. D & F: §6.2, # 11, p. 215
4. D & F: §6.2, # 13, p. 215
5. Find the subgroup lattice for the group Z₇₂. Given the two subnormal series
   {0}≤ <4> ≤ < Z₇₂
   and
   {0}≤ <18> ≤ <6> ≤ < Z₇₂
   follow the proof of Schreier's theorem to find refinements of each series and exhibit the isomorphic factor groups, precisely as in the proof.
6. D & F: §5.1, # 5, p. 158
7. D & F: §5.5, # 6, p. 186
8. D & F: §3.3, # 7, p. 187