Math 420/620
Homework 5
Fall 1999
- If
has finite index
in the group
, then show that there is a normal subgroup ![](Image521.gif)
, with
and
.
- Classify all groups of order
with
a nonzero prime number.
- Let
be distinct odd primes with ![](Image527.gif)
- Assume that
does not divide
, classify all groups of order ![](Image530.gif)
- (G)
Classify all groups of order ![](Image531.gif)
without the above assumption.
- Let
be a group of order
for a nonzero prime
. Prove that
has subgroups of or
der
for all ![](Image535.gif)
- 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 ![](Image540.gif)
.