It has been proved in Janssens, Jespers, and Temmerman [Proc. Amer. Math. Soc. 145 (2017), pp. 2771–2783] that if
h
h
is an element of prime order
p
p
in a finite nilpotent group
G
G
and
u
=
h
+
(
h
−
1
)
g
h
^
∈
Z
G
u=h+(h-1)g\widehat {h}\in \mathbb {Z}G
,
u
∉
G
u\not \in G
, then
⟨
u
∗
,
u
⟩
≈
C
p
∗
C
p
\langle u^*,u\rangle \approx C_p\ast C_p
. We offer a simple geometric approach to generalize this result.