Solutions to HW1
1. Denote by S3 the nonabelian group of order 6. How many homomorphisms are there
from S3 to S3 ? List them all.
Solution. Let : S3 S3 be a homomorphism. Then ker is one of the three normal
subgroups of S3 . We consider these three cases
Review: Basic Terminology and Results
Also: Group Actions
(Handout January 12, 2009)
A multiplicative group is a set G on which multiplication is dened (and closed, so that
xy G for all x, y G) such that
(i) For all x, y, z G, we have (xy )z = x(yz ).