aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence...

theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations of groups on...

mathematical finite group theory, an N-group is a group all of whose local subgroups (that is, the normalizers of nontrivial p-subgroups) are solvable groups. The...

{\displaystyle P} . In this case the theory of automorphisms of a finite cyclic group can be used. Another special case is when n {\displaystyle n} is...

classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either cyclic...

complete classification of finite simple groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, and...

mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points...

In group theory, a discipline within abstract algebra, a special group is a finite group of prime power order that is either elementary abelian itself...

classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the...

combinatorial group theory. A presentation is said to be finitely generated if S is finite and finitely related if R is finite. If both are finite it is said...

In the theory of algebraic groups, a special group is a linear algebraic group G with the property that every principal G-bundle is locally trivial in...

representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which...

automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The...

In the mathematical classification of finite simple groups, a thin group is a finite group such that for every odd prime number p, the Sylow p-subgroups...

quotient space is finite. crystallographic point group congruence subgroup arithmetic group geometric group theory computational group theory freely discontinuous...

known as group theory, the term Z-group refers to a number of distinct types of groups: in the study of finite groups, a Z-group is a finite group whose...

group theory, a nilpotent group G is a group that has an upper central series that terminates with G. Equivalently, it has a central series of finite...

representation theory; this special case has very different properties. See Representation theory of finite groups. Compact groups or locally compact groups — Many...

study the group. It is mostly of interest for the study of infinite groups. Special cases of groups with finiteness properties are finitely generated...

alternating group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of degree...

Minkowski's theorem Topological group Field Finite field Galois theory Grothendieck group Group ring Group with operators Heap Linear algebra Magma Module...

In group theory, a branch of mathematics, a core is any of certain special normal subgroups of a group. The two most common types are the normal core...

of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also...

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...

of finite simple groups says that most finite simple groups arise as the group G(k) of k-rational points of a simple algebraic group G over a finite field...

model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley...

finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups,...

FC-group A group is an FC-group if every conjugacy class of its elements has finite cardinality. finite group A finite group is a group of finite order, that...

affine group of an affine space over a finite field of prime order. Groups similar to Galois groups are (today) called permutation groups. The theory of permutation...

when A is a finitely generated Z-algebra. (The groups Gn(A) are the K-groups of the category of finitely generated A-modules) Additive K-theory Bloch's formula...