Abstract
Suppose that G is a finite solvable group and V is a finite, faithful and completely reducible G-module. Let H be an odd-order subgroup of G, then H has at least two regular orbits on V ⊕ V . Suppose in addition that | V | is odd, then there exists v ∈ V in a regular orbit of F ( G ) ∩ H such that C H ( v ) ⊆ F 2 ( G ) . Let G be a solvable group, H be an odd-order Hall π-subgroup of G, V be a faithful G-module, over possibly different finite fields of odd π-characteristic and assume that V O π ( G ) is completely reducible, then there exists v ∈ V such that C H ( v ) ⊆ O π ( G ) .
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.
