العربية
中国
Français
Deutsch
Ελληνική
हिन्दी
Italiano
日本語
Português
Русский
EspañolCARTER SUBGROUP
In mathematics, a 'Carter subgroup' of a finite group ''G'' is a subgroup ''H'' that is a nilpotent group, and self-normalizing. These subgroups were introduced by Roger Carter.
Any finite solvable group has a Carter subgroup, and any two Carter subgroups of a finite solvable group are conjugate subgroups (and therefore isomorphic, ''a fortiori'').
The alternating group A5 of order 60 is an example that has no Carter subgroups.
★ Cartan subalgebra
★ R.W. Carter, ''Nilpotent selfnormalizing subgroups of soluble groups'' Math. Z. , 75 : 2 (1961) pp. 136–139
★ B. Huppert, ''Endliche Gruppen'' , 1 , Springer (1979) pp. 482–490
★
Any finite solvable group has a Carter subgroup, and any two Carter subgroups of a finite solvable group are conjugate subgroups (and therefore isomorphic, ''a fortiori'').
The alternating group A5 of order 60 is an example that has no Carter subgroups.
| Contents |
| See also |
| References |
See also
★ Cartan subalgebra
References
★ R.W. Carter, ''Nilpotent selfnormalizing subgroups of soluble groups'' Math. Z. , 75 : 2 (1961) pp. 136–139
★ B. Huppert, ''Endliche Gruppen'' , 1 , Springer (1979) pp. 482–490
★
This article provided by Wikipedia. To edit the contents of this article, click here for original source.
psst.. try this: add to faves
