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Difference between revisions of "Subnormal subgroup"

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''attainable subgroup''
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#REDIRECT [[Subnormal series]]
 
 
Any member of any [[subnormal series]] of a group. To indicate the subnormality of a subgroup $H$ in a group $G$, the notation $H \lhd\!\lhd G$ is used.
 
 
 
====References====
 
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<TR><TD valign="top">[1]</TD> <TD valign="top">  M.I. Kargapolov,  J.I. [Yu.I. Merzlyakov] Merzljakov,  "Fundamentals of the theory of groups" , Springer  (1979)  (Translated from Russian)</TD></TR>
 
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====Comments====
 
A subnormal subgroup is also called a subinvariant subgroup.
 
 
 
A subnormal subgroup of $G$ that coincides with its commutator subgroup and whose quotient by its centre is simple is called a component of $G$. The product of all components of $G$ is known as the layer of $G$. It is an important [[characteristic subgroup]] of $G$ in the theory of finite simple groups, see e.g. [[#References|[a1]]].
 
 
 
====References====
 
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Suzuki,  "Group theory" , '''1–2''' , Springer  (1986)</TD></TR>
 
<TR><TD valign="top">[a2]</TD> <TD valign="top">  J.C. Lennox,  S.E. Stonehewer,  "Subnormal subgroups of groups" , Clarendon Press  (1987)</TD></TR>
 
<TR><TD valign="top">[a3]</TD> <TD valign="top">  D.J.S. Robinson,  "A course in the theory of groups" , Springer  (1982)</TD></TR>
 
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Latest revision as of 09:54, 3 January 2021

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How to Cite This Entry:
Subnormal subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subnormal_subgroup&oldid=51196
This article was adapted from an original article by N.N. Vil'yams (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article