Christofides algorithm: Difference between revisions

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Let me first begin by introducing myself. My title is Boyd Butts even though it is not the name on my birth certificate. South Dakota is where I've always been living. For many years I've been working as a payroll clerk. The preferred hobby for my children and me is to play baseball but I haven't made a dime with it.<br><br>Here is my web page :: [http://www.breda.nl/users/noeliadfebdftijfsdnt www.breda.nl]
In [[mathematics]], in the field of [[group theory]], a [[subgroup]] <math>H</math> of a [[group (mathematics)|group]] <math>G</math> is termed '''malnormal''' if for any <math>x</math> in <math>G</math> but not in <math>H</math>, <math>H</math> and <math>H^x</math> intersect in the [[identity element]].
 
Some facts about malnormality:
 
*An intersection of malnormal subgroups is malnormal.
*Malnormality is [[transitive relation|transitive]], that is, a malnormal subgroup of a malnormal subgroup is malnormal.
*The trivial subgroup and the whole group are malnormal subgroups. A [[normal subgroup]] that is also malnormal must be one of these.
*Every malnormal subgroup is a special type of [[C-group]] called a trivial intersection subgroup or TI subgroup.
 
When  G  is finite, a malnormal subgroup  H  distinct from 1 and G is called a "Frobenius complement"; the set  N  of elements of  G  which are, either equal to 1, or non-conjugate to any
element of  G,  is a normal subgroup of  G, called the "Frobenius kernel", and  G  is the semi-direct product of  H  and  N (Frobenius' theorem, see e.g. [Feit pp.133-139]).
 
Reference:
 
W. Feit, Characters of finite groups, Benjamin Publ., New York, 1967.
 
 
{{DEFAULTSORT:Malnormal Subgroup}}
[[Category:Subgroup properties]]

Revision as of 14:35, 4 February 2014

Let me first begin by introducing myself. My title is Boyd Butts even though it is not the name on my birth certificate. South Dakota is where I've always been living. For many years I've been working as a payroll clerk. The preferred hobby for my children and me is to play baseball but I haven't made a dime with it.

Here is my web page :: www.breda.nl

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