Affine extensions of loops
نویسندگان
چکیده
منابع مشابه
C-loops: Extensions and Constructions
C-loops are loops satisfying the identity x(y · yz) = (xy · y)z. We develop the theory of extensions of C-loops, and characterize all nuclear extensions provided the nucleus is an abelian group. C-loops with central squares have very transparent extensions; they can be built from small blocks arising from the underlying Steiner triple system. Using these extensions, we decide for which abelian ...
متن کاملAbelian Extensions and Solvable Loops
Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated...
متن کاملFlag-transitive Extensions of Dual Affine Planes
(with 1 , q , ̀ ) . An infinite family of simply connected examples for this diagram with q 5 2 is obtained by truncating Coxeter complexes of type D n . Two dif ferent finite families with three members and q 5 4 arise from the Steiner systems for the Mathieu groups M 2 2 , M 2 3 and M 2 4 . The geometries of these two families are simply connected . Three more simply connected examples of rank...
متن کاملEigenvectors-based parallelisation of nested loops with affine dependences
Abstract This paper presents a method for parallelising nested loops with affine dependences. The data dependences of a program are represented exactly using a dependence matrix rather than an imprecise dependence abstraction. By a careful analysis of the eigenvectors and eigenvalues of the dependence matrix, we detect the parallelism inherent in the program, partition the iteration space of th...
متن کاملAffine-by-Statement Transformations of Imperfectly Nested Loops
A majority of loop restructuring techniques developed so far assume that loops are perfectly nested. The unimodular approach unifies three individual transformations – loop interchange, skewing and reversal – but is still limited to perfect loop nests. This paper outlines a framework that enables the use of unimodular transformations to restructure imperfect loop nests. The concepts previously ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
سال: 2004
ISSN: 0025-5858,1865-8784
DOI: 10.1007/bf02941531