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The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

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, ...

C_3 is the unique group of group order 3. It is both Abelian and cyclic. Examples include the point groups C_3, C_(3v), and C_(3h) and the integers under addition modulo 3 ...

C_5 is the unique group of group order 5, which is Abelian. Examples include the point group C_5 and the integers mod 5 under addition (Z_5). No modulo multiplication group ...

C_7 is the cyclic group that is the unique group of group order 7. Examples include the point group C_7 and the integers modulo 7 under addition (Z_7). No modulo ...

The finite group C_2×C_6 is the finite group of order 12 that is the group direct product of the cyclic group C2 and cyclic group C6. It is one of the two Abelian groups of ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

The free module of rank n over a nonzero unit ring R, usually denoted R^n, is the set of all sequences {a_1,a_2,...,a_n} that can be formed by picking n (not necessarily ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

A solvable group is a group having a normal series such that each normal factor is Abelian. The special case of a solvable finite group is a group whose composition indices ...