Math 420/620
Fall 1999
Homework 6
- Construct every semidirect product of
with itself.
- Show that
(where
denotes semidirect product).
- (G)
Assume that
is cyclic,
is arbitrary and
and
are homomorphisms from
into
such that
and
are conjugate subgroups of
Show that
.
- Let
be a
-group of order
for some
. Show that for all
, ![](Image582.gif)
- Classify all groups of order:
- 12.
- (G)
18.
- Find all abelian groups of order 2160.
- Give an example of a finite nonabelian group that cannot be written as a semidirect product of two of its proper subgroups.
- (G)
Classify all groups of order
for any prime ![](Image584.gif)