Abstract
In this paper, we study the normal complement problem on semisimple group algebras and modular group algebras [Formula: see text] over a field [Formula: see text] of positive characteristic. We provide an infinite class of abelian groups [Formula: see text] and Galois fields [Formula: see text] that have normal complement in the unit group [Formula: see text] for semisimple group algebras [Formula: see text]. For metacyclic group [Formula: see text] of order [Formula: see text], where [Formula: see text] are distinct primes, we prove that [Formula: see text] does not have normal complement in [Formula: see text] for finite semisimple group algebra [Formula: see text]. Finally, we study the normal complement problem for modular group algebras over field of characteristic 2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
