Difference between revisions of "Subnormal series"

of a group \$G\$

A subgroup series of \$G\$, \$\$ E = G_0 \le G_1 \le \cdots \le G_n = G \$\$ where each subgroup \$G_i\$ is a normal subgroup of \$G_{i+1}\$. The quotient groups \$G_{i+1}/G_i\$ are called factors, and the number \$n\$ is called the length of the subnormal series. Infinite subnormal series have also been studied (see Subgroup system). A subnormal series that cannot be refined further is called a composition series, and its factors are called composition factors.