Wikipedia:
Carter 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.
See also
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 (2001), "Carter subgroup", in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 1-55608-010-7
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