Powerful 2-Engel Groups

Primož Moravec, Gunnar Traustason

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We study powerful 2-Engel groups. We show that every powerful 2-Engel group generated by three elements is nilpotent of class at most two. Surprisingly, the result does not hold when the number of generators is larger than three. In this article and its sequel, we classify powerful 2-Engel groups of class 3 that are minimal in the sense that every proper powerful section is nilpotent of class at most 2.
Original languageEnglish
Pages (from-to)4096-4119
Number of pages24
JournalCommunications in Algebra
Issue number11
Publication statusPublished - Nov 2008


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