ag.algebraic geometry - Is an algebraic space group always a scheme?

Over a field, the reference is indeed "Algebraization of formal moduli, I".

Over a base more general than a field, the answer may be no. For example, Artin proved in "Algebraization of formal moduli, I" that under some natural conditions the Picard functor is representable by an algebraic space (it is a group algebraic space of course). There are several sufficient conditions for it to be a scheme, due to Artin and Mumford. You will find a discussion, if not the proof, of them in Bosch-Lutkebohmert-Raynaud's "Neron models". But in general case is not known, I think.

On the other hand, abelian algebraic spaces over a scheme S (i.e. smooth proper with irreducible geometric fibers) is an abelian scheme over S. See p.3 of Faltings-Chai's "Degenerations of abelian varieties", where this is attributed to Raynaud and Deligne.