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The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...

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 ...

A cyclic group is a group that can be generated by a single element X (the group generator). Cyclic groups are Abelian. A cyclic group of finite group order n is denoted C_n, ...

The Lorentz group is the group L of time-preserving linear isometries of Minkowski space R^((3,1)) with the Minkowski metric dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2 ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

Direct search factorization is the simplest (and most simple-minded) prime factorization algorithm. It consists of searching for factors of a number by systematically ...

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...

The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...