In 2012, Guo and Gong prove that if G is a finite non-abelian group with -G- = 1, then jG : Z-G-j < jG′jjU-G-j, in which U-G- is the nilpotent residual of G. In the present work, we prove that the assumption of finite- ness of the group can be omitted. Moreover, we state some properties of groups G for which n+1-G- \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ Zn-G- = 1 in the spacial case -G- = 1.

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