Ad
related to: group theory mathematics questions
Search results
Results From The WOW.Com Content Network
Plus teacher and student package: Group Theory This package brings together all the articles on group theory from Plus, the online mathematics magazine produced by the Millennium Mathematics Project at the University of Cambridge, exploring applications and recent breakthroughs, and giving explicit definitions and examples of groups.
The existence of the free Burnside group and its uniqueness up to an isomorphism are established by standard techniques of group theory. Thus if G is any finitely generated group of exponent n, then G is a homomorphic image of B(m, n), where m is the number of generators of G. The Burnside problem for groups with bounded exponent can now be ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.
The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics (for example quark theory) grew steadily in the twentieth century. In rough terms, Lie group theory is the common ground of group theory and the theory of topological manifolds .
In mathematics, the classification of finite simple groups (popularly called the enormous theorem [1] [2]) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group ...
Saharon Shelah showed that, given the canonical ZFC axiom system, the problem is independent of the usual axioms of set theory. [1] More precisely, he showed that: If every set is constructible, then every Whitehead group is free; If Martin's axiom and the negation of the continuum hypothesis both hold, then there is a non-free Whitehead group.
The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra. As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.