Abstract
In this paper, firstly, we determine the local 2-GCI-property and 2−GCI-property of the cyclic group. Then, for the dihedral group D2n, we prove that it has local GCI-property if and only if n is an odd prime or 9. Further, the dihedral group D2n cannot have GCI-property. Moreover, we discuss the GCI-property of the elementary abelian group, the dicyclic group and the semi-dihedral group.
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