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The reciprocal differences are closely related to the divided difference. The first few are explicitly given by rho(x_0,x_1)=(x_0-x_1)/(f_0-f_1) (1) ...

f_p=f_0+1/2p(p+1)delta_(1/2)-1/2(p-1)pdelta_(-1/2) +(S_3+S_4)delta_(1/2)^3+(S_3-S_4)delta_(-1/2)^3+..., (1) for p in [-1/2,1/2], where delta is the central difference and ...

If p^k is the highest power of a prime p dividing the order of a finite group G, then a subgroup of G of order p^k is called a Sylow p-subgroup of G.

A p-elementary subgroup of a finite group G is a subgroup H which is the group direct product H=C_n×P, where P is a p-group, C_n is a cyclic group, and p does not divide n.

The order of a finite field is the number of elements it contains.

The sporadic group HJ, also denoted J_2.

A prime field is a finite field GF(p) for p is prime.

The Tits group is a group of order 17971200. It is implemented in the Wolfram Language as TitsGroupT[].

X is a p^'-group if p does not divide the group order of X.

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...