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The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.
It consists of all the elements of E that can be obtained by repeatedly using the operations +, −, *, / on the elements of F and S. If E = F(S), we say that E is generated by S over F. Primitive element An element α of an extension field E over a field F is called a primitive element if E=F(α), the smallest extension field containing α.
A Latin square, the unbordered multiplication table for a quasigroup whose 10 elements are the digits 0–9. The multiplication table of a finite quasigroup is a Latin square: an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.
Éléments de mathématique (English: Elements of Mathematics) is a series of mathematics books written by the pseudonymous French collective Nicolas Bourbaki. Begun in 1939, the series has been published in several volumes, and remains in progress. The series is noted as a large-scale, self-contained, formal treatment of mathematics. [1] [2]
The field with one element is then defined to be F 1 = {0, 1}, the multiplicative monoid of the field with two elements, which is initial in the category of multiplicative monoids. A monoid ideal in a monoid A is a subset I that is multiplicatively closed, contains 0, and such that IA = { ra : r ∈ I , a ∈ A } = I .
In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups of cyclotomic fields. A special case was first proven by Ernst Kummer ( 1847 ) while the general result is due to Ludwig Stickelberger ( 1890 ).
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In mathematics, the projective special linear group PSL(2, 7), isomorphic to GL(3, 2), is a finite simple group that has important applications in algebra, geometry, and number theory. It is the automorphism group of the Klein quartic as well as the symmetry group of the Fano plane .
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