# Subnormal series

From Encyclopedia of Mathematics

*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*.

#### Comments

A subnormal series is also called a subinvariant series.

#### References

[a1] | M. Hall jr., "The theory of groups" , Macmillan (1959) pp. Sect. 8.4 Zbl 0084.02202 Zbl 0919.20001 |

**How to Cite This Entry:**

Subnormal series.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Subnormal_series&oldid=42885

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article