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Two groups G and H are said to be isoclinic if there are isomorphisms G/Z(G)->H/Z(H) and G^'->H^', where Z(G) is the group center of the group, which identify the two ...

Two partially ordered sets are said to be isomorphic if their "structures" are entirely analogous. Formally, partially ordered sets P=(X,<=) and Q=(X^',<=^') are isomorphic ...

A sequence {a_j} of positive integers is called an iteration sequence if there exists a strictly increasing sequence {s_k} of positive integers such that a_1=s_1>=2 and ...

The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G. Note that while Itô's theorem was ...

Applying the Kaprekar routine to 4-digit number reaches 0 for exactly 77 4-digit numbers, while the remainder give 6174 in at most 8 iterations. The value 6174 is sometimes ...

Let G be a group, then there exists a piecewise linear knot K^(n-2) in S^n for n>=5 with G=pi_1(S^n-K) iff G satisfies 1. G is finitely presentable, 2. The Abelianization of ...

Approximations to Khinchin's constant include K = -(ln85181832)/(tan8) (1) = 1/(29)sqrt(6065) (2) = 6-sqrt(ln59055) (3) = 18^(27/79), (4) which are correct to 9, 7, 6, and 5 ...

A set of plane measure 0 that contains a circle of every radius.

The Kinoshita-Terasaka knot is the prime knot on eleven crossings with braid word ...

The determinant of a knot is defined as |Delta(-1)|, where Delta(z) is the Alexander polynomial (Rolfsen 1976, p. 213).