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For any prime number p and any positive integer n, the p^n-rank r_(p^n)(G) of a finitely generated Abelian group G is the number of copies of the cyclic group Z_(p^n) ...

The special unitary group SU_n(q) is the set of n×n unitary matrices with determinant +1 (having n^2-1 independent parameters). SU(2) is homeomorphic with the orthogonal ...

The cyclic group C_(10) is the unique Abelian group of group order 10 (the other order-10 group being the non-Abelian D_5). Examples include the integers modulo 10 under ...

The cyclic group C_9 is one of the two Abelian groups of group order 9 (the other order-9 Abelian group being C_3×C_3; there are no non-Abelian groups of order 9). An example ...

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

A linear algebraic group is a matrix group that is also an affine variety. In particular, its elements satisfy polynomial equations. The group operations are required to be ...

Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

Let G be an algebraic group. G together with the discrete topology is a locally compact group and one may consider the counting measure as a left invariant Haar measure on G. ...

C_5 is the unique group of group order 5, which is Abelian. Examples include the point group C_5 and the integers mod 5 under addition (Z_5). No modulo multiplication group ...

The equation x_1^2+x_2^2+...+x_n^2-2x_0x_infty=0 represents an n-dimensional hypersphere S^n as a quadratic hypersurface in an (n+1)-dimensional real projective space ...