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A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

In the Minkowski space of special relativity, a four-vector is a four-element vector x^mu=(x^0,x^1,x^2,x^3) that transforms under a Lorentz transformation like the position ...

The wreathed product of the monster group by Z_2. The bimonster is a quotient of the Coxeter group with the above Coxeter-Dynkin diagram. This had been conjectured by Conway, ...

The Janko groups are the four sporadic groups J_1, J_2, J_3 and J_4. The Janko group J_2 is also known as the Hall-Janko group. The Janko groups are implemented in the ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

A rational homomorphism phi:G->G^' defined over a field is called an isogeny when dimG=dimG^'. Two groups G and G^' are then called isogenous if there exists a third group ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

The composition quotient groups belonging to two composition series of a finite group G are, apart from their sequence, isomorphic in pairs. In other words, if I subset H_s ...

The twistor equation states that del _(A^')^((A)phi^(B...E))=0, where the parentheses denote symmetrization, in a Lorentz transformation, primed spinors transform under the ...

A short exact sequence of groups A, B, and C is given by two maps alpha:A->B and beta:B->C and is written 0->A->B->C->0. (1) Because it is an exact sequence, alpha is ...