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Details for article 4 of 7 found articles
| Title: |
Quelques consequences de la locale nilpotence des boucles de moufang commutatives |
| Author: |
Beneteau, Lucien |
| Appeared in: |
Communications in algebra |
| Paging: | Volume 11 (1983) nr. 15 pages 1725-1753 |
| Year: |
1983 |
| Contents: |
It is well-known that any finitely generated commutative Moufang loop (CML) is centrally nilpotent and has a finite derived subloop. Consequently such a loop possesses all the classical properties of noethe-rianity: any subloop is finitely generated too, any surjective endomorphism is an automorphism, etc. Besides we prove that, in any CML E(finitely generated or not) the maximal subloops are normal of prime index ; thus the Frattini quotient E/Φ(E) is an abelian group, sub-direct product of groups of prime order. We shall study also some dual notion of the Frattini subloop, namely the subloop φ*(E) generated by the minimal normal subloops ; it turns out that φ*(E) is made up by the products of the prime order central elements. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 4 of 7 found articles
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