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If x is a member of a set A, then x is said to be an element of A, written x in A. If x is not an element of A, this is written x not in A. The term element also refers to a ...

The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

Let G be group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x<y, then x in I. For k disjoint chains in which the ith chain ...

The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

Let A be a C^*-algebra, then an element a in A is called normal if aa^*=a^*a.

A function element is an ordered pair (f,U) where U is a disk D(Z_0,r) and f is an analytic function defined on U. If W is an open set, then a function element in W is a pair ...