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| − | ''attainable subgroup''
| + | #REDIRECT [[Subnormal series]] |
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| − | 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.
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| − | ====References====
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| − | <table>
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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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| − | </table>
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| − | ====Comments====
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| − | A subnormal subgroup is also called a subinvariant subgroup.
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| − | 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]]].
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| − | ====References====
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| − | <table>
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| − | <TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Suzuki, "Group theory" , '''1–2''' , Springer (1986)</TD></TR>
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| − | <TR><TD valign="top">[a2]</TD> <TD valign="top"> J.C. Lennox, S.E. Stonehewer, "Subnormal subgroups of groups" , Clarendon Press (1987)</TD></TR>
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| − | <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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| − | </table>
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| − | {{TEX|done}}
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Latest revision as of 09:54, 3 January 2021
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