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A word is said to be overlapfree if it has no subwords of the form xyxyx. A squarefree word is overlapfree, and an overlapfree word is cubefree. The numbers t(n) of binary ...

Rule 62 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

L is a subnormal subgroup of H if there is a "normal series" (in the sense of Jordan-Hölder) from L to H.

Given the direct sum of additive Abelian groups A direct sum B, A and B are called direct summands. The map i_1:A-->A direct sum B defined by i(a)=a direct sum 0 is called ...

A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their automorphism groups.

A semigroup with a noncommutative product in which no product can ever be expressed more simply in terms of other elements.

Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups C_2 and D_1 are ...

Any finite semigroup is a divisor for an alternating wreath product of finite groups and semigroups.

Krohn-Rhodes theory is a mathematical approach that seeks to decompose finite semigroups in terms of finite aperiodic semigroups and finite groups.