Let $G$ be a finite group and let $g \in G$ be an element of order $pq$, where $p < q$ are prime numbers. Denote by $g^G$ the conjugacy class of $g$ in $G$. Under which conditions does the following hold?: $$ |(g^p)^G| = |(g^q)^G| = |(g^{q−p})^G| $$ -- Is it possible that this happens?
Finite groups which have elements $g$ of order $pq$ such that the sizes of the conjugacy classes of $g^p$, of $g^q$ and of $g^{q-p}$ coincide
Anna
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