In mathematics, the Schreier refinement theorem of group theory states that any two normal series of subgroups of a given group have equivalent refinements.
The theorem is named after the Austrian mathematician Otto Schreier who proved it in 1928. It provides an elegant proof of the Jordan–Hölder theorem.
Famous quotes containing the words refinement and/or theorem:
“You know that your toddler needed love and approval but he often seemed not to care whether he got it or not and never seemed to know how to earn it. Your pre-school child is positively asking you to tell him what does and does not earn approval, so he is ready to learn any social refinement of being human which you will teach him....He knows now that he wants your love and he has learned how to ask for it.”
—Penelope Leach (20th century)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)