Week 8 homework, Math 446.
1. Prove that the group presented by <a,b| abA=b^2, baB=a^2> is
the trivial group
(where aA=bB=1, i.e. A=a^(-1)= the inverse of A).
2. Prove that the Burnside group B(n,2)=<g1,...,gn | g^2=1, such
that g is in <g1...gn> > is finite.
0.5.7.3, 0.5.7.4, 0.5.7.5, 0.5.8.1
Puzzle: Can one give a geometric explanation for the Cayley graph of
the permutation
group of {Tao, Hartrich, Cynamon, Atkinson}, with generators
{switch 1st & 2nd, switch
2nd & 3rd, switch 3rd and 4th}?