The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group 𝔽ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [𝔽ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups $Γ =⟨a₁,...,a_{r}⟩⊂ ℚ *$, with and $a_{i} ≤ T_{i}$, with a range of uniformity...