Let a 1 , a, be a sequence of elements in a semigroup G Then there exists a unique function N G such that (1) a 1 , (2) a 1 a 2 , (3) (a 1 a 2 )a 3 and for n 1,(n 1) ((n))a n 1 Note that (n) is precisely the standard n product 72 II i 1 ai ...

ANSWER The given sequence of elements in a semigroup G can be expressed as a product of the elements ...

Let a 1 , a, ... be a sequence of elements in a semigroup G. Then there

Question:

Let a₁, a, ... be a sequence of elements in a semigroup G. Then there exists a unique function ψ : N* → G such that ψ(1) = a₁, ψ(2) = a₁a₂, ψ(3) = (a₁a₂)a₃ and for n ≥ 1,ψ(n + 1) = (ψ(n))a_n+1- Note that ψ(n) is precisely the standard n product