Abstract
A finite group G is said to be an SCLD-group if every square of conjugacy class lengths of elements of G divides the order |G|. In this note, we prove that a non-abelian SCLD-group is not a simple group, an almost simple group or a Frobenius group. For a nilpotent group G, G is an SCLD-group if and only if each Sylow subgroup of G is an SCLD-group. A group of order p n for the prime p and n ≤ 4i s an SCLD-group. We also provide some other results on SCLD-groups.
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