Bygeneralizingthewhiskertopologyonthe nthhomotopygroupofpointedspace(X,x0), denoted by πwh n (X,x0), we show that πwh n (X,x0) is a topological group if n ≥ 2. Also,we present some necessary and sufficient conditions for πwh n (X,x0) to be discrete, Hausdorff and indiscrete. Then we prove that Ln(X,x0) the natural epimorphic image of the Hawaiian group Hn(X,x0) is equal to the set of all classes of convergent sequences to the identity in πwh n (X,x0). As a consequence, we show that Ln(X,x0) ∼ = Ln(Y,y0) if πwh n (X,x0)∼ = πwh n (Y,y0), buttheconversedoesnotholdingeneral, exceptforsomeconditions. Also,weshowthatonsomeclassesofspacessuchassemilocally n-simplyconnected spaces and n-Hawaiian like spaces, the whisker topology and the topology induced by the compact-open topology of n-loop space coincide. Finally, we show that n-SLT paths can transfer πwh n and hence Ln isomorphically along its points.

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