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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 ...
[r] A group action gives further means to study the object being acted on. [s] On the other hand, it also yields information about the group. Group representations are an organizing principle in the theory of finite groups, Lie groups, algebraic groups and topological groups, especially (locally) compact groups. [63] [65]
The reactivity of a functional group can be modified by other functional groups nearby. Functional group interconversion can be used in retrosynthetic analysis to plan organic synthesis. A functional group is a group of atoms in a molecule with distinctive chemical properties, regardless of the other atoms in the molecule.
In chemistry, a group (also known as a family) [1] is a column of elements in the periodic table of the chemical elements. There are 18 numbered groups in the periodic table; the 14 f-block columns, between groups 2 and 3, are not numbered.
More generally, the fundamental group of a bouquet of r circles is the free group on r letters. The fundamental group of a wedge sum of two path connected spaces X and Y can be computed as the free product of the individual fundamental groups: () ().
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 ...
which can be understood as "The orthogonal group O(n + 1) acts transitively on the unit sphere S n, and the stabilizer of a point (thought of as a unit vector) is the orthogonal group of the perpendicular complement, which is an orthogonal group one dimension lower."
In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication.This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group.