Let α= (1234) and β= (24) ε S4, What is βα?
a) Find |α| and |β|
b) Find H= < α , β>
c) Find |H|
2) Show that (Q, +) is not finitely generated.
3) Let G denote a group such that |G| < 200. Suppose G has subgroups of order 25 and 35. Find the order of G.
4) Give an example of a noncommutative group in which every
subgroup is normal
5) Let G denote a group. Let H < G be a subgroup of G such that H Z(G). Show that if G/H is cyclic then G=Z(G), i.e., G is commutative