infinite subgroup
101Nielsen–Schreier theorem — In group theory, a branch of mathematics, the Nielsen–Schreier theorem is the statement that every subgroup of a free group is itself free.[1][2][3] It is named after Jakob Nielsen and Otto Schreier. Contents …
102Equivalence relation — In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. Let a , b , and c be arbitrary elements of some set X . Then a b or a ≡ b denotes that a is… …
103Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …
104Topological group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
105Sporadic group — In the mathematical field of group theory, a sporadic group is one of the 26 exceptional groups in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the subgroup consisting… …
106Cayley graph — In mathematics, the Cayley graph, also known as the Cayley colour graph, is the graph that encodes the structure of a discrete group. Its definition is suggested by Cayley s theorem (named after Arthur Cayley) and uses a particular, usually… …
107Frieze group — A frieze group is a mathematical concept to classify designs on two dimensional surfaces which are repetitive in one direction, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. The… …
108Divisible group — In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive… …
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 …
110Lagrange's theorem (group theory) — Lagrange s theorem, in the mathematics of group theory, states that for any finite group G , the order (number of elements) of every subgroup H of G divides the order of G . Lagrange s theorem is named after Joseph Lagrange. Proof of Lagrange s… …
