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I want to check if a generator of $Z^_m$ has the same degree in $Z^_m /$ < p > (quotient group).

Is there any way to do that?

I want to check if a generator of $Z^$ Z^_m$ _m $ has the same degree in $Z^$ Z^_m /$ / $ < p > (quotient group).

Is there any way to do that? that?

I want to check if a generator of $ Z^$Z^_m $ _m$ has the same degree in $ Z^$Z^_m / $ /$ < p > (quotient group).

Is there any way to do that?

I want to check if a generator of $Z^Z^_m$ _m has the same degree in $Z^Z^_m /$ / < p > (quotient group).

Is there any way to do that?

I want to check if a generator of Z^_m has the same degree in Z^_m / < p > (quotient group).

Is there any way to do that?

I want to check if a generator of Z^_m Z^star_m has the same degree in Z^_m Z^star_m / < p > (quotient group).

Is there any way to do that?

I want to check if a generator of Z^star_m $\mathbb{Z}^\star_m$ has the same degree in Z^star_m $\mathbb{Z}^\star_m / < \langle p > \rangle$ (quotient group).

Is there any way to do that?