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A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

An invariant series of a group G is a normal series I=A_0<|A_1<|...<|A_r=G such that each A_i<|G, where H<|G means that H is a normal subgroup of G.

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

A group of four elements, also called a quadruplet or tetrad.

An Auslander algebra which connects the representation theories of the symmetric group of permutations and the general linear group GL(n,C). Schur algebras are ...

An exact sequence is a sequence of maps alpha_i:A_i->A_(i+1) (1) between a sequence of spaces A_i, which satisfies Im(alpha_i)=Ker(alpha_(i+1)), (2) where Im denotes the ...

The word population has a number of distinct but closely related meanings in statistics. 1. A finite and actually existing group of objects which, although possibly large, ...

The wallpaper groups are the 17 possible plane symmetry groups. They are commonly represented using Hermann-Mauguin-like symbols or in orbifold notation (Zwillinger 1995, p. ...

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...