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The group of all nonsingular n×n stochastic matrices over a field F. It is denoted S(n,F). If p is prime and F is the finite field of order q=p^m, S(n,q) is written instead ...

The Harada-Norton group is the sporadic group HN of order |HN| = 273030912000000 (1) = 2^(14)·3^6·5^6·7·11·19. (2) It is implemented in the Wolfram Language as ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

C_3 is the unique group of group order 3. It is both Abelian and cyclic. Examples include the point groups C_3, C_(3v), and C_(3h) and the integers under addition modulo 3 ...

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of ...

C_4 is one of the two groups of group order 4. Like C_2×C_2, it is Abelian, but unlike C_2×C_2, it is a cyclic. Examples include the point groups C_4 (note that the same ...

Two representations of a group chi_i and chi_j are said to be orthogonal if sum_(R)chi_i(R)chi_j(R)=0 for i!=j, where the sum is over all elements R of the representation.

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

The group D_5 is one of the two groups of order 10. Unlike the cyclic group C_(10), D_5 is non-Abelian. The molecule ruthenocene (C_5H_5)_2Ru belongs to the group D_(5h), ...

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...