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In the original formulation, a quantity associated with ideal class groups. According to Chevalley's formulation, a Grössencharakter is a multiplicative character of the ...

Let sigma(n) be the divisor function. Then lim sup_(n->infty)(sigma(n))/(nlnlnn)=e^gamma, where gamma is the Euler-Mascheroni constant. Ramanujan independently discovered a ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

A group automorphism is an isomorphism from a group to itself. If G is a finite multiplicative group, an automorphism of G can be described as a way of rewriting its ...

A group action G×Omega->Omega might preserve a special kind of partition of Omega called a system of blocks. A block is a subset Delta of Omega such that for any group ...

The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...