The best unbiased estimators in the absence of sufficiency and completeness

In this study, a simple generalization of the Lehmann-Scheffe theorem is proposed in cases where UMVUEs exist but a sufficiently complete statistics does not exist. Also, another method is introduced based on the group action. In this method, UMVUE for the unknown parameter is found using  a commutative and associative binary operation.  Finally, the motivation for using the words "completeness" and "unbiasedness" is expressed in such a way that completeness and unbiasedness are not characteristic of a statistic or its parametric form, but a family of distributions of a statistic, and deleting even one point of the parameter space may change the completeness.