- recursively presented group
- рекурсивно определённая группа
English-Russian scientific dictionary. 2008.
English-Russian scientific dictionary. 2008.
Presentation of a group — In mathematics, one method of defining a group is by a presentation. One specifies a set S of generators so that every element of the group can be written as a product of some of these generators, and a set R of relations among those generators.… … Wikipedia
Rank of a group — For the dimension of the Cartan subgroup, see Rank of a Lie group In the mathematical subject of group theory, the rank of a group G , denoted rank( G ), can refer to the smallest cardinality of a generating set for G , that is:… … Wikipedia
Algebraically closed group — In mathematics, in the realm of group theory, a group A is algebraically closed if any finite set of equations and inequations that make sense in A already have a solution in A . This idea will be made precise later in the article.Informal… … Wikipedia
Absolute presentation of a group — In mathematics, one method of defining a group is by an absolute presentation.B. Neumann, The isomorphism problem for algebraically closed groups, in: Word Problems, Decision Problems, and the Burnside Problem in Group Theory, Amsterdam London… … Wikipedia
Grigorchuk group — In the mathematical area of group theory, the Grigorchuk group or the first Grigorchuk group is a finitely generated group constructed by Rostislav Grigorchuk that provided the first example of a finitely generated group of intermediate (that is … Wikipedia
Word problem for groups — In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented group G is the algorithmic problem of deciding whether two words represent the same element. Although it… … Wikipedia
Higman's embedding theorem — In group theory, Higman s embedding theorem states that every finitely generated recursively presented group R can be embedded as a subgroup of some finitely presented group G . This is a result of Graham Higman from the 1960s. [ Graham Higman,… … Wikipedia
HNN extension — In mathematics, the HNN extension is a basic construction of combinatorial group theory.Introduced in a 1949 paper Embedding Theorems for Groups [ cite journal|title=Embedding Theorems for Groups|journal=Jornal of the London Mathematical… … Wikipedia
Recursion theory — Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability… … Wikipedia
Computability theory — For the concept of computability, see Computability. Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown … Wikipedia
Undecidable problem — In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct an algorithm that leads to a yes or no answer the problem is not decidable.A decision problem is any … Wikipedia