Abstract
We describe some group theory which is useful in the classification of combinatorial objects having given groups of automorphisms. In particular, we show the usefulness of the concept of a friendly subgroup: a subgroup H of a group K is a friendly subgroup of K if every subgroup of K isomorphic to H is conjugate in K to H . We explore easy-to-test sufficient conditions for a subgroup H to be a friendly subgroup of a finite group K , and for this, present an algorithm for determining whether a finite group H is a Sylow tower group. We also classify the maximal partial spreads invariant under a group of order 5 in both PG(3,7) and PG (3,8).
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.
