Non averaging sequences in finite groups

Let us say that a non averaging sequence in a group G is a sequence x1,,xn such that
x2ixjxk
for any indices i,j,k such that two at least are distinct. My question is: given n, what is the smallest group having a non-averaging sequence of length n?

Has this question been already tackled in the literature, maybe under a different name?

There are some partial results (we can build cyclic groups with non-averaging sequence based on the existence of non-averaging sequences in Z), but I would like to know if there exist more “optimal” results.

Answer

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Source : Link , Question Author : vizietto , Answer Author : Community

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