In this paper we prove three theorems, each of which gives a set of absolutely independent group axioms. Theorem 2 is an extension of Morgado's theorem obtained by using a weaker associativity axiom. The axioms of Theorem 3 are the first absolutely independent group axioms we have encountered for ,,~ich there is no k such that the axioms are absolutely independent (rood k) [2, p. 758]. The systems of Jacobson-Yoco~n and Morgado and the systems which appear in Theorems 1 and 2 of this paper are absolutely independent (rood ,~0). We conclude the paper with two axioms which define a group and which are very [l] (and in this case absolutely) independent (rood n) for every integer n ~ 1. We will write "xy" instead of " x , y" in all proofs. The following lemma is quite useful.