Abstract
LetG andG φ be isomorphic groups. We introduce and study a quotient ν(G) of the free productG *G φ which is a group extention of the non-abelian tensor squareG ⊗G. This seems to bring computational advantages to calculate this last group. Looking over ν as an operator in the class of groups we prove that it preserves properties of the argumentG such as finiteness, set of prime divisors, nilpotency and solvability. For a finitep-groupG we find a good polynomial bound for the order of ν (G).
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Rocco, N.R. On a construction related to the non-abelian tensor square of a group. Bol. Soc. Bras. Mat 22, 63–79 (1991). https://doi.org/10.1007/BF01244898
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DOI: https://doi.org/10.1007/BF01244898