Year: 2026
Type: article
Abstract: We give an affirmative answer to the Grunwald problem for new families of nonsolvable finite groups G , away from the set of primes dividing | G | . Furthermore, we show that such G verify the condition (BM), that is, the Brauer–Manin obstruction to weak approximation is the only one for quotients of SL n by G . These new families include extensions of groups satisfying (BM) by kernels which are products of symmetric groups 𝔖 m , with m ≠ 2 , 6 , and alternating groups 𝔄 5 . We also investigate (BM) for small groups by giving an explicit list of small order groups for which (BM) is unknown and we show that for many of them (BM) holds under Schinzel’s hypothesis.
Source: Annales de l’institut Fourier
DOI: 10.5802/aif.3784
Authors: Elyes Boughattas, Danny Neftin
Institutions: University of Bath, Technion – Israel Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G3257303119
OpenAlex ID: W7140830213