Free groups and semigroups in \(\beta\) N (Q791681)

The most striking conclusions of this paper are easy to state. It is well known that \(\beta\) N, the Stone-Čech compactification of the positive integers with addition, has a natural semigroup structure. It is also known that \(\beta\) N is non-commutative. Indeed its centre is N. We prove that it is very non-commutative; it contains copies of the free group on \(2^ c\) generators. As a by-product of our methods, we obtain simpler proofs than have so far been given that the numbers of minimal left and of minimal right ideals in \(\beta\) N are both \(2^ c\).