Classification of finite solvable CN-groups

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This article gives the statement, and possibly proof, of a statement where the conclusion of the statement involves a disjunction (OR) of two possibilities. The prototypical form is: "every A is a B or a C."

Statement

Suppose G is a finite group that is both a finite solvable group and a CN-group (hence also a finite CN-group. Then, G must be of one of these three types:

  1. G is a finite nilpotent group.
  2. G is a Frobenius group where the Frobenius complement is a finite group in which every abelian subgroup is cyclic.
  3. G is a 3-step group.

Proof

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References

Textbook references