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ON NONABELIAN TENSOR ANALOGUES OF 2-ENGEL CONDITIONS

Published online by Cambridge University Press:  31 January 2005

PRIMOŽ MORAVEC
PRIMOŽ MORAVEC
Affiliation:
Department of Mathematics, Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia e-mail: primoz.moravec@fmf.uni-lj.si
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Abstract

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Tensor analogues of right 2-Engel elements in groups were introduced by D. P. Biddle and L.-C. Kappe. We investigate the properties of right 2-Engel tensor elements and introduce the concept of $2_{\otimes}$-Engel margin. With the help of these results we describe the structure of $2_{\otimes}$-Engel groups. In particular, we prove a tensor version of Levi's theorem for 2-Engel groups and determine tensor squares of two-generator $2_{\otimes}$-Engel $p$-groups.

Keywords

20F4520F99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 1 , January 2005 , pp. 77 - 86
Copyright
2005 Glasgow Mathematical Journal Trust

Footnotes

This work was supported by the Ministry of Education, Science and Sport of Slovenia.