Group problems

nowits

1. The problem statement, all variables and given/known data
Let G be a group and let #G=77. Prove the following:
a) G is cyclic, if there is such an element a in G that a²¹≠1 and a²²≠1
b) If there are such elements a and b, so that ord(a)=7 and ord(b)=11, then G=<a,b>

2. Relevant equations, 3. The attempt at a solution
I really don't even know where to begin with these. So I'd appreciate if someone could point me in the right direction.

HallsofIvy

You do understand, don't you, that any proper subgroups must be of order 7 and 11? And that are subgroups of those orders? That should make (b) trivial.

As for (a) the crucial point is that 21= 3*7 and 22= 2*11.