Carter subgroup

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In mathematics, a Carter subgroup of a finite group is a self-normalizing nilpotent subgroup. They 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 (and therefore isomorphic).

The alternating group A5 of order 60 has no Carter subgroups.

[edit] See also

[edit] 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
  • N.N. Vil'yams, "Carter subgroup" SpringerLink Encyclopaedia of Mathematics (2001)
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