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Subnormal series

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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