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free 2-engel groups

Proceedings of the Edinburgh Mathematical Society (1)

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ON COMPUTING THE NON-ABELIAN TENSOR SQUARES OF THE FREE 2-ENGEL GROUPS
Russell D. Blyth, Robert Fitzgerald Morse, Joanne L. Redden
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Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 2 / June 2004

Published online by Cambridge University Press:

01 July 2004, pp. 305-323
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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