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Let G be a group of odd order that contains a non-central element x whose order is either a prime p ≥ 5 or 3l, with l ≥ 2. Then, in 
, the group of units of ℤG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that 〈um, vm〉 = 〈um〉 ∗ 〈vm〉 ≌ ℤ ∗ ℤ
