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The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

Consider the Euclid numbers defined by E_k=1+p_k#, where p_k is the kth prime and p# is the primorial. The first few values of E_k are 3, 7, 31, 211, 2311, 30031, 510511, ... ...

The Gram series is an approximation to the prime counting function given by G(x)=1+sum_(k=1)^infty((lnx)^k)/(kk!zeta(k+1)), (1) where zeta(z) is the Riemann zeta function ...

A set (usually of letters) from which a subset is drawn. A sequence of letters is called a word, and a set of words is called a code.

An archaic name for topology.

Two algebraic objects that are commutative, i.e., A and B such that A*B=B*A for some operation *, are said to commute with each other.

Always increasing; never remaining constant or decreasing. Also called strictly increasing.

A line segment on the boundary of a face, also called a side.

Theta(G;A)=<theta(a):a in A-1> is an A-invariant solvable p^'-subgroup of G.

A transversal line is a line which intersects each of a given set of other lines. It is also called a semisecant.