On locally finite -groups satisfying an Engel condition |
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Authors: | Alireza Abdollahi Gunnar Traustason |
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Institution: | Department of Mathematics, University of Isfahan, Isfahan 81744, Iran ; C.M.I.-Université de Provence, UMR-CNRS 6632, 39, rue F. Joliot-Curie, 13453 Marseille Cedex 13, France |
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Abstract: | For a given positive integer and a given prime number , let be the integer satisfying . We show that every locally finite -group, satisfying the -Engel identity, is (nilpotent of -bounded class)-by-(finite exponent) where the best upper bound for the exponent is either or if is odd. When the best upper bound is or . In the second part of the paper we focus our attention on -Engel groups. With the aid of the results of the first part we show that every -Engel -group is soluble and the derived length is bounded by some constant. |
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Keywords: | Locally finite $p$-groups Engel groups |
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