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A finite group is called Z-sequenceable if its non-identity elements can be listed $x_1,x_2,\mathrm{\cdots },x_n$ so that $x_i{x}_{i+1}=x_{i+1}{x}_i$ for $i=1,2,\mathrm{\cdots },n\mathrm{—}1$. Various conditions are determined for a group G to be Z-sequenceable. Moreover several well known classes of groups which satisfy such conditions are found out.