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The convolution of two complex-valued functions on a group G is defined as (a*b)(g)=sum_(k in G)a(k)b(k^(-1)g) where the support (set which is not zero) of each function is ...

The set of points of X fixed by a group action are called the group's set of fixed points, defined by {x:gx=x for all g in G}. In some cases, there may not be a group action, ...

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 ...

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 ...

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

If G is a group, then the torsion elements Tor(G) of G (also called the torsion of G) are defined to be the set of elements g in G such that g^n=e for some natural number n, ...

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

A knot move illustrated above. Two knots cannot be distinguished using Vassiliev invariants of order <=n iff they are related by a sequence of such moves (Habiro 2000). There ...

A symmetric block design (4n+3, 2n+1, n) which is equivalent to a Hadamard matrix of order 4n+4. It is conjectured that Hadamard designs exist for all integers n>0, but this ...

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.