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ON COMPUTING THE NON-ABELIAN TENSOR SQUARES OF THE FREE 2-ENGEL GROUPS

Published online by Cambridge University Press:  01 July 2004

Russell D. Blyth ,
Robert Fitzgerald Morse  and
Joanne L. Redden
Russell D. Blyth
Affiliation:
Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, USA
Robert Fitzgerald Morse
Affiliation:
Department of Electrical Engineering and Computer Science, University of Evansville, Evansville, IN 47722, USA ([email protected])
Joanne L. Redden
Affiliation:
Department of Mathematics, University of Evansville, Evansville, IN 47722, USA
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Abstract

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In this paper we compute the non-abelian tensor square for the free 2-Engel group of rank $n>3$. The non-abelian tensor square for this group is a direct product of a free abelian group and a nilpotent group of class 2 whose derived subgroup has exponent 3. We also compute the non-abelian tensor square for one of the group’s finite homomorphic images, namely, the Burnside group of rank $n$ and exponent 3.

AMS 2000 Mathematics subject classification: Primary 20F05; 20F45. Secondary 20F18

Keywords

non-abelian tensor squarefree 2-Engel groupsBurnside groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 305 - 323
Copyright
Copyright © Edinburgh Mathematical Society 2004