Arne Georg is listed as "h. o. ä. son" or "hennes oäkta son" (her illegitimate son). But in the probate record after August Georg Öhman, Arne Georg is indeed listed as one of his heirs. See:
I don't know what this means (if he could have been adopted by August Georg as a son, or if he must have been the actual father?) but I thought I might as well send you the information.