1. ## Order of element

Let H be a group in which h²=I for all h is an element of H.
Prove: Suppose |H|<∞. Let {h₁,h₂,…..hn} be minimal set of generators for H. then

2. Originally Posted by apple2009
Let H be a group in which h²=I for all h is an element of H.
Prove: Suppose |H|<∞. Let {h₁,h₂,…..hn} be minimal set of generators for H. then

Any element is a product of $h_1,...,h_n$ and since H is abelian (why?) we can even order that product in ascending index order:
$h_1^{\epsilon_1}\cdot...\cdot h_n^{\epsilon_n}\,,\,\,with\,\,\,\epsilon_i=0\,\,o r\,\, 1$
Well, in how many ways can you choose the first factor in such a product? In how many the second factor?....

Tonio