Elementary abelian group
In mathematics, specifically in group theory, an elementary abelian group (or elementary abelian p-group) is an abelian group in which every nontrivial element has order p. The number p must be prime,
Power closed
In mathematics a p-group is called power closed if for every section of the product of powers is again a th power. Regular p-groups are an example of power closed groups. On the other hand, powerful p
Commutator collecting process
In group theory, a branch of mathematics, the commutator collecting process is a method for writing an element of a group as a product of generators and their higher commutators arranged in a certain
Prüfer group
In mathematics, specifically in group theory, the Prüfer p-group or the p-quasicyclic group or p∞-group, Z(p∞), for a prime number p is the unique p-group in which every element has p different p-th r
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 Peter Ludwig Sylow that give detailed informat
Hall–Petresco identity
In mathematics, the Hall–Petresco identity (sometimes misspelled Hall–Petrescu identity) is an identity holding in any group. It was introduced by Hall and Petresco. It can be proved using the commuta
Regular p-group
In mathematical finite group theory, the concept of regular p-group captures some of the more important properties of abelian p-groups, but is general enough to include most "small" p-groups. Regular
Focal subgroup theorem
In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in and is the "first major application
Pro-p group
In mathematics, a pro-p group (for some prime number p) is a profinite group such that for any open normal subgroup the quotient group is a p-group. Note that, as profinite groups are compact, the ope
Descendant tree (group theory)
In mathematics, specifically group theory, a descendant tree is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of prime power order ,
P-group generation algorithm
In mathematics, specifically group theory, finite groups of prime power order , for a fixed prime number and varying integer exponents , are briefly called finite p-groups. The p-group generation algo
Powerful p-group
In mathematics, in the field of group theory, especially in the study of p-groups and pro-p-groups, the concept of powerful p-groups plays an important role. They were introduced in, where a number of
P-group
In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a
Coclass
In mathematics, the coclass of a finite p-group of order pn is n − c, where c is the class.
Special group (finite group theory)
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 or of class 2 with its derived group, its center,
Tarski monster group
In the area of modern algebra known as group theory, a Tarski monster group, named for Alfred Tarski, is an infinite group G, such that every proper subgroup H of G, other than the identity subgroup,
Extra special group
In group theory, a branch of abstract algebra, extraspecial groups are analogues of the Heisenberg group over finite fields whose size is a prime. For each prime p and positive integer n there are exa
P-core
No description available.