Remark

(5) The definition of an exact sequence extends immediately to groups which are not necessarily commutative; in this case of course multiplicative notation is used with 0 replaced by 1 in the formulae (if no confusion arises). Parts (a), (b), (c) of Proposition 3 are still valid and also (d) when F is a normal subgroup of E. Remark 2 and Proposition 3(e) hold on condition that $f(E)$ is a normal subgroup of F; Remarks 3 and 4 are valid without modification.