  We study and extend the conditions for asociativity on fusion over
antielement free $\sigma$-sets to introduce a group to solve $\sigma$-set
equations. $\sigma$-sets as a theory of sets and antisets is sumarized and used
as a framework to define the main elements of this work. A theorem on Local
Asociativity, conmutative groups and solution of one variable fusion equation
is presented.
