abelian-by-nilpotent group

См. также в других словарях:

• Nilpotent group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Abelian group — For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… …   Wikipedia

• Group 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… …   Wikipedia

• Solvable group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• p-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… …   Wikipedia

• A-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… …   Wikipedia

• Heisenberg 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… …   Wikipedia

• P-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. That is, for each element g of the group, there exists a nonnegative integer n such that g to the power pn is equal to the …   Wikipedia

• Core (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… …   Wikipedia

• Glossary of group theory — A group ( G , •) is a set G closed under a binary operation • satisfying the following 3 axioms:* Associativity : For all a , b and c in G , ( a • b ) • c = a • ( b • c ). * Identity element : There exists an e ∈ G such that for all a in G , e •… …   Wikipedia

• Multiplicative group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia