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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 ...

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. ...

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 ...

Let Gamma be a representation for a group of group order h, then sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). The proof is ...

The projective special linear group PSL_n(q) is the group obtained from the special linear group SL_n(q) on factoring by the scalar matrices contained in that group. It is ...

A primitive subgroup of the symmetric group S_n is equal to either the alternating group A_n or S_n whenever it contains at least one permutation which is a q-cycle for some ...