** Burnside's lemma, a theorem of group theory

** Burnside's problem, about the sizes of finite group mathematics

** Well-ordering theorem: Every set can be well-ordered.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.

** Tychonoff's theorem stating that every product of compact topological spaces is compact.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

** Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.

** The Nielsen – Schreier theorem, that every subgroup of a free group is free.

** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals

** The theorem that every Hilbert space has an orthonormal basis.

** The Banach – Alaoglu theorem about compactness of sets of functionals.

** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.

** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.

** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.

** Hilbert's basis theorem

** Bayes ' theorem

** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.

** Lyapunov's central limit theorem

** Superposition theorem, in electronics

** " Kelvin's vorticity theorem for incompressible or barotropic flow ".

** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem

** Various proofs of the four colour theorem.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).

** Terminology of the British Isles, discusses the sometimes ambiguous or contentious names for parts of the island group

** The B-52's ( album ), an album by the eponymous group

** School band, a group of student musicians who rehearse and perform instrumental music together

** Marching band, a group of performers that consist of instrumental musicians who generally perform outdoors and incorporate some type of marching ( and possibly other movements ) with their musical performance

** Han Chinese, the dominant ethnic group in mainland China, Taiwan and Singapore

** the exceptional and twisted groups of Lie type ( including the Tits group ).

** Religion and blood group with RH factor

** Religion ( or " NRE " if none ) and blood group with RH factor

** Blood group with RH factor

** First and middle initials and suffix ; blood group

** Social Security number with no dashes or spaces followed immediately by " USN ", space, blood group

** Blood group

** Fermentative hydrogen production, the fermentative conversion of organic substrate to biohydrogen manifested by a diverse group of bacteria

** The Pferdestärke PS ( German translation of horsepower ) is a name for a group of similar power measurements used in Germany around the end of the 19th century, all of about one metric horsepower in size.

** Propithecus diadema group

** Propithecus verreauxi group

** Parabolic induction: a method of constructing group representations of a reductive group from representations of its parabolic subgroups.

** five lectures, heard by the group, as blip. tv videos

** Diagnosis-related group

** Kuru ( archaeology ), an Indo-Aryan ethnic group

** Order † Sparassodonta ( formerly viewed as marsupials, now as a sister group of metatherians )