Abstract
The introduction of group theory in the sixth form often raises the question of its relationship with other areas of mathematics. The purpose of this note is to develop a group theoretical solution of a simply described counting problem; a problem which may, in fact, be solved in several other ways. The development of the solution yields useful examples of several algebraic notions; in particular the notion of equivalence relation is exploited in a variety of ways. The particular group theoretical/combinatorial result that finally yields the answer to our problem is known as Burnside’s Lemma. This result is not normally presented until a second or third year university course. I hope to convince the reader that the manner of presentation given here is perfectly accessible at a more elementary level.
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.
