Classification of finite solvable CN-groups
From Groupprops
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 is a finite group that is both a finite solvable group and a CN-group (hence also a finite CN-group. Then, must be of one of these three types:
- is a finite nilpotent group.
- is a Frobenius group where the Frobenius complement is a finite group in which every abelian subgroup is cyclic.
- is a 3-step group.
Proof
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Textbook references
- Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 402, Theorem 14.1.5, ^{More info}