factor 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 factor groups. The elements of G/N are written N a and form a group under the normal operation on the group N on the coefficient a. Thus, (N a)(N b) = N a b.

Abhyankar's conjecture | backslash | coset | extension field | Lagrange's group theorem | normal subgroup | outer automorphism group | subgroup