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The study of a finite group G using the local subgroups of G. Local group theory plays a critical role in the classification theorem of finite groups.

A number triangle of order n with entries 1 to n such that entries are nondecreasing across rows and down columns and all entries in column j are less than or equal to j. An ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

An important result in ergodic theory. It states that any two "Bernoulli schemes" with the same measure-theoretic entropy are measure-theoretically isomorphic.

An inner automorphism of a group G is an automorphism of the form phi(g)=h^(-1)gh, where h is a fixed element of G. An outer automorphism of G is an automorphism which cannot ...

A parabolic cyclide formed by inversion of a ring torus when the inversion sphere is tangent to the torus.

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

1 and -1 are the only integers which divide every integer. They are therefore called the prime units.