Search results
Results from the WOW.Com Content Network
If a set is such that it cannot be endowed with a group structure, then it is necessarily non-wellorderable. Otherwise the construction in the second section does yield a group structure. However these properties are not equivalent. Namely, it is possible for sets which cannot be well-ordered to have a group structure.
In 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. Groups recur throughout mathematics, and the methods ...
The set of diffeomorphisms of M that preserve a G-structure is called the automorphism group of that structure. For an O(n)-structure they are the group of isometries of the Riemannian metric and for an SL(n,R)-structure volume preserving maps. Let P be a G-structure on a manifold M, and Q a G-structure on a manifold N.
For any cocommutative Hopf algebra, an element g is called group-like if Δg = g ⊗ g and εg = 1, and the group-like elements form a group under multiplication. In the case of the Hopf algebra of a formal group law over a ring, the group like elements are exactly those of the form
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
There is a convenient relationship between the kernel and cokernel and the abelian group structure on the hom-sets. Given parallel morphisms f and g, the equaliser of f and g is just the kernel of g − f, if either exists, and the analogous fact is true for coequalisers. The alternative term "difference kernel" for binary equalisers derives ...