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14 relations: Burnside theorem, Complement (group theory), Coprime integers, Formation (group theory), Group (mathematics), Index of a subgroup, London Mathematical Society, Mathematics, Order (group theory), Schur–Zassenhaus theorem, Semidirect product, Simple group, Solvable group, Sylow theorems.
Burnside theorem
In mathematics, Burnside theorem in group theory states that if G is a finite group of order where p and q are prime numbers, and a and b are non-negative integers, then G is solvable.
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Complement (group theory)
In mathematics, especially in the area of algebra known as group theory, a complement of a subgroup H in a group G is a subgroup K of G such that Equivalently, every element of G has a unique expression as a product hk where h ∈ H and k ∈ K. This relation is symmetrical: if K is a complement of H, then H is a complement of K. Neither H nor K need be a normal subgroup of G.
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Coprime integers
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
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Formation (group theory)
In mathematical group theory, a formation is a class of groups closed under taking images and such that if G/M and G/N are in the formation then so is G/M∩N.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Index of a subgroup
In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively half of the elements of G lie in H. The index of H in G is usually denoted |G: H| or or (G:H).
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London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Order (group theory)
In group theory, a branch of mathematics, the term order is used in two unrelated senses.
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Schur–Zassenhaus theorem
The Schur–Zassenhaus theorem is a theorem in group theory which states that if G is a finite group, and N is a normal subgroup whose order is coprime to the order of the quotient group G/N, then G is a semidirect product (or split extension) of N and G/N.
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Semidirect product
In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product.
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Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.
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Solvable group
In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions.
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Sylow theorems
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (1872) that give detailed information about the number of subgroups of fixed order that a given finite group contains.
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