Math 420/620
Homework 5
Fall 1999
- If has finite index in the group , then show that there is a normal subgroup , with and .
- Classify all groups of order with a nonzero prime number.
- Let be distinct odd primes with
- Assume that does not divide , classify all groups of order
- (G)
Classify all groups of order
without the above assumption.
- Let be a group of order for a nonzero prime . Prove that has subgroups of or
der for all
- How many elements of order 7 must a simple group of order 168 have?
- If , 2907, or 6545, show that is not simple.
- (G)
Let with distinct primes. Show is not simple.
- (G)
Show if is a
nonabelian simple group of order less than 100, then
.