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ON SUBGROUPS RELATED TO THE TENSOR CENTER

Published online by Cambridge University Press:  31 July 2003

DAVID P. BIDDLE  and
LUISE-CHARLOTTE KAPPE
DAVID P. BIDDLE
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA e-mail: biddle@math.cotnell.edu
LUISE-CHARLOTTE KAPPE
Affiliation:
Department of Mathematical Sciences, SUNY at Binghamton, Binghamton, NY 13902-6000, USA e-mail: menger@math.binghamton.edu
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Abstract

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The tensor center of a group $G$ is the set of elements $a$ in $G$ such that $a\otimes g = 1_\otimes$ for all $g$ in $G$. It is a characteristic subgroup of $G$ contained in its center. We introduce tensor analogues of various other subgroups of a group such as centralizers and 2-Engel elements and investigate their embedding in the group as well as interrelationships between those subgroups.

Keywords

20F99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 2 , May 2003 , pp. 323 - 332
Copyright
2003 Glasgow Mathematical Journal Trust