3-step group implies solvable CN-group

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., 3-step group) must also satisfy the second group property (i.e., finite solvable group)
View all group property implications | View all group property non-implications
Get more facts about 3-step group|Get more facts about finite solvable group

This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., 3-step group) must also satisfy the second group property (i.e., CN-group)
View all group property implications | View all group property non-implications
Get more facts about 3-step group|Get more facts about CN-group

Statement

Suppose $G$ is a finite group that is a 3-step group for a prime number $p$. Then, $G$ is a solvable group (i.e., a finite solvable group) and also a CN-group.

Proof

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References

Textbook references

• Finite Groups by Daniel Gorenstein, ISBN 0821843427, Page 401, Lemma 14.1.4, ^{More info}