# Subnormal series

From Encyclopedia of Mathematics

*of a group *

A subgroup series of ,

where each subgroup is a normal subgroup of . The quotient groups are called factors, and the number 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 |

**How to Cite This Entry:**

Subnormal series.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Subnormal_series&oldid=19288

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