nilpotent group
1Nilpotent group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
2Nilpotent — This article is about a type of element in a ring. For the type of group, see Nilpotent group. In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that xn = 0. The term was… …
3Nilpotent orbit — Nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple Lie groups and semisimple Lie algebras. Contents 1 Definition 2 Examples 3 Properties …
4Group scheme — In mathematics, a group scheme is a group object in the category of schemes. That is, it is a scheme G with the equivalent properties* there is a group law expressible as a multiplication μ and inversion map ι on G ; or * G is a functor (as in… …
5Core (group) — 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 subgroup and the p core of a group. Contents 1 The normal core 1.1 Definition 1.2… …
6Solvable group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
7Heisenberg group — In mathematics, the Heisenberg group, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form or its generalizations under the operation of matrix multiplication. Elements a, b, c can be taken from some… …
8Engel group — In mathematics, an element x of a Lie group or a Lie algebra is called an n Engel element, named after Friedrich Engel, if it satisfies the n Engel condition that the repeated commutator [ x , y ] , y ] , ..., y ] with n copies of y is trivial… …
9p-group — Not to be confused with n group. In mathematics, given a prime number p, a p group is a periodic group in which each element has a power of p as its order: each element is of prime power order. That is, for each element g of the group, there… …
10A-group — In mathematics, in the area of abstract algebra known as group theory, an A group is a type of group that is similar to abelian groups. The groups were first studied in the 1940s by Philip Hall, and are still studied today. A great deal is known… …
