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The American Mathematical Society awards two prizes named in honor of Prof. Frank Nelson Cole, a senior member of the AMS who made a bequest to the society in 1928 upon his ...

A characteristic factor is a factor in a particular factorization of the totient function phi(n) such that the product of characteristic factors gives the representation of a ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

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 ...

Every finite Abelian group can be written as a group direct product of cyclic groups of prime power group orders. In fact, the number of nonisomorphic Abelian finite groups ...

The pair group of a group G is the group that acts on the 2-subsets of {1,...,p} whose permutations are induced by G. Pair groups can be calculated using PairGroup[g] in the ...

The projective special orthogonal group PSO_n(q) is the group obtained from the special orthogonal group SO_n(q) on factoring by the scalar matrices contained in that group. ...

The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. ...

For a group G and a normal subgroup N of G, the quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...