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R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data. R software is open-source and free software.
R group may refer to: In chemistry: Pendant group or side group; Side chain; Substituent; In mathematics: Tempered representation This page was last edited on ...
The following definitions have been used in the literature to define a divisible module M over a ring R: rM = M for all nonzero r in R. [9] (It is sometimes required that r is not a zero-divisor, and some authors [10] require that R is a domain.) For every principal left ideal Ra, any homomorphism from Ra into M extends to a homomorphism from R ...
Compared to libraries in other programming languages, R packages must conform to a relatively strict specification. [3] The Writing R Extensions manual [7] specifies a standard directory structure for R source code, data, documentation, and package metadata, which enables them to be installed and loaded using R's in-built package management ...
For example, the dihedral group D 8 of order sixteen can be generated by a rotation, r, of order 8; and a flip, f, of order 2; and certainly any element of D 8 is a product of r ' s and f ' s. However, we have, for example, rfr = f −1, r 7 = r −1, etc., so such products are not unique in D 8. Each such product equivalence can be expressed ...
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Cauchy's theorem is generalized by Sylow's first theorem, which implies that if p n is the maximal power of p dividing the order of G, then G has a subgroup of order p n (and using the fact that a p-group is solvable, one can show that G has subgroups of order p r for any r less than or equal to n).
The zeroth algebraic K group () of a (not necessarily commutative) ring R is the Grothendieck group of the monoid consisting of isomorphism classes of finitely generated projective modules over R, with the monoid operation given by the direct sum. Then is a covariant functor from rings to abelian groups.