Subnormal series

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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.


A subnormal series is also called a subinvariant series.


[a1] M. Hall jr., "The theory of groups" , Macmillan (1959) pp. Sect. 8.4
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Subnormal series. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article