# Carter subgroup

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A maximal nilpotent subgroup of a group that coincides with its normalizer. Introduced by R. Carter [1]. Any finite solvable group has a Carter subgroup, and all Carter subgroups of are conjugate (Carter's theorem).

#### References

 [1] R.W. Carter, "Nilpotent selfnormalizing subgroups of soluble groups" Math. Z. , 75 : 2 (1961) pp. 136–139 [2] A.I. Kostrikin, "Finite groups" Itogi Nauk. Algebra 1964 (1966) pp. 7–46 (In Russian)