We investigate integral Galois stable representations of finite groups over local and global fields and their integers under the ground field extensions related to permutation modules. We consider normal extensions E/F and subgroups G ⊂ GLn(E) stable under the natural operation of the Galois group of E/F with some extra integrality conditions. The possible realization fields of G with these integrality conditions are of special interest, and we consider certain criteria of integrality for representations in GLn(E). We also study a series of related arithmetic problems and examples.
J. Jaraden, J. and Malinin, Dmitry
"On Some Finite Arithmetic Groups and Generalized Permutation Modules,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 13.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss4/13