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=42878
Subnormal series. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subnormal_series&oldid=42878
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article