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math.GR2018
The loop of formal power series with noncommutative coefficients under substitution
José M. Pérez-Izquierdo
The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We initiate the study of this loop by de…
math.GR2016★ 1 cited
On torsion-free nilpotent loops
J. Mostovoy, J. M. Perez-Izquierdo, I. P. Shestakov
We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most,…
math.GR2004★ 2 cited
Dimension filtration on loops
J. Mostovoy, J. M. Pérez-Izquierdo
We show that the graded group associated to the dimension filtration on a loop acquires the structure of a Sabinin algebra after being tensored with a field of characteristic zero.…