background: since most clinical treatments of persian children’s language impairments are based on either the therapist, clinicians’ experiences (mostly), or english language norms (sometimes), comparing two minor indices of speech quality, namely “mean length of utterance” (mlu) and “mean length of five phrasal utterances” (mlfpu) between different age groups of children, would be unequivocall...

Given a free product of groups G=⁎j∈JAj and natural number n, what is the minimal possible commutator length an element gn∈G not conjugate to elements factors? We give exhaustive answer this question.