Let be $m$ an integer, $m>0$, $n=p_1^{a_1}...p_t^{a_t}$. I define $f(n)=a_1+...+a_t$. Let $G$ be a finite group and define $f(G)=max(f(|g|):g\in G)$.

Is there a finite solvable group $G$ with $f(exp (G))>3f(G)?$

And, in general, is there a finite solvable group $G$ with $f(exp (G))>nf(G)$, for each $n \in \mathbb{N}?$

Let be $m$ an integer, $m>0$, $n=p_1^{a_1}...p_t^{a_t}$. Define $f(n)=a_1+...+a_t$. Let $G$ be a finite group and define $f(G)=\max\left\{\,f(\lvert g\rvert):g\in G\,\right\}$.

Is there a finite solvable group $G$ with $f(\exp (G))>3\,f(G)?$

And, in general, is there a finite solvable group $G$ with $f(\exp(G))>n\,f(G)$, for each $n \in \mathbb{N}?$

Let be $m$ an integer, $m>0$, $n=p_1^{a_1}...p_t^{a_t}$. I define $f(n)=a_1+...+a_t$. Let be $G$ a finite group and I define $f(G)=max(f(|g|):g\in G)$.

Is there a finite solvable group $G$ with $f(exp (G))>3f(G)?$

And, in general, is there a finite solvable group $G$ with $f(exp (G))>nf(G)$, for each $n \in \mathbb{N}?$

Let be $m$ an integer, $m>0$, $n=p_1^{a_1}...p_t^{a_t}$. I define $f(n)=a_1+...+a_t$. Let $G$ be a finite group and define $f(G)=max(f(|g|):g\in G)$.

Is there a finite solvable group $G$ with $f(exp (G))>3f(G)?$

And, in general, is there a finite solvable group $G$ with $f(exp (G))>nf(G)$, for each $n \in \mathbb{N}?$