Locally nilpotent 4-Engel groups are Fitting groups. (Q1418999)
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scientific article; zbMATH DE number 2026914
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Locally nilpotent 4-Engel groups are Fitting groups. |
scientific article; zbMATH DE number 2026914 |
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Locally nilpotent 4-Engel groups are Fitting groups. (English)
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14 January 2004
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A group \(G\) is a Fitting group of degree \(n\) if all normal closures of elements of \(G\) are nilpotent of class at most \(n\). The author proves that locally nilpotent 4-Engel groups are Fitting groups of degree at most 4; if there are no elements of order 2 or 5, the Fitting degree is bounded by 3 (Theorem 6.8). The arguments are done via Lie algebras, and the primes 2, 3 and 5 have to be considered separately.
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Engel conditions
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locally nilpotent groups
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Fitting groups
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Fitting degrees
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