Solvable
101Erdős–Straus conjecture — The Erdős–Straus conjecture states that for all integers n ≥ 2, the rational number 4/ n can be expressed as the sum of three unit fractions. That is, there exist positive integers x , y , and z such that :frac4n = frac1x + frac1y + frac1z.The… …
102BRST algorithm — Boender Rinnooy Stougie Timmer algorithm (BRST) is an optimization algorithm suitable for finding global optimum of black box functions. In their paper Boender et al cite journal | author = Boender, C.G.E., A.H.G. Rinnooy Kan, L. Strougie and G.T …
103Karp-Lipton theorem — The Karp–Lipton theorem in complexity theory states that if the boolean satisfiability problem (SAT) can be solved by Boolean circuits with a polynomial number of logic gates, then :Pi 2 , = Sigma 2 , and therefore mathrm{PH} , = Sigma 2 ,.That… …
104Proof of impossibility — A proof of impossibility, sometimes called a negative proof or negative result , is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general. Often proofs of impossibility have put to rest decades or… …
105Polycyclic group — In mathematics, especially in the area of abstract algebra known as group theory, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated).Equivalently, a group G is… …
106Entropy (arrow of time) — Entropy is the only quantity in the physical sciences that picks a particular direction for time, sometimes called an arrow of time. As one goes forward in time, the second law of thermodynamics says that the entropy of an isolated system can… …
107Supersolvable group — In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvablility is stronger than the notion of solvability.DefinitionLet G be a group. G is supersolvable… …
108Cubic reciprocity — is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q) is solvable; the word reciprocity comes from the form of the main theorem, which states that …
109Problems in loop theory and quasigroup theory — In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Many …
110Tits alternative — In mathematics, the Tits alternative, named for Jacques Tits, is an important theorem about the structure of finitely generated linear groups. It states that every such group is either virtually solvable (i.e. has a solvable subgroup of finite… …
