On Some Finite Arithmetic Groups and Generalized Permutation Modules

Authors

J. J. Jaraden, Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia\\ Department of Mathematics and Statistics, Al-Hussein Bin Talal University, Ma’an, JordanFollow
Dmitry Malinin, Department of Mathematics, UWI, Mona Campus, Kingston, JamaicaFollow

Author Country (or Countries)

Jordan

Abstract

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.

Recommended Citation

J. Jaraden, J. and Malinin, Dmitry (2015) "On Some Finite Arithmetic Groups and Generalized Permutation Modules," Applied Mathematics & Information Sciences: Vol. 09: Iss. 4, Article 13.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss4/13