Groups Satisfying the Converse to Lagrange's Theorem

Author

Jonah N. Henry, Missouri State UniversityFollow

Date of Graduation

Fall 2019

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Abstract

Lagrange’s theorem, which is taught early on in group theory courses, states that the order of a subgroup must divide the order of the group which contains it. In this thesis, we consider the converse to this statement. A group satisfying the converse to Lagrange’s theorem is called a CLT group. We begin with results that help show that a group is CLT, and explore basic CLT groups with examples. We then give the conditions to guarantee either CLT is satisfied or a non-CLT group exists for more advanced cases. Additionally, we show that CLT groups are properly contained between supersolvable and solvable groups.

Keywords

lagrange, group, subgroup, order, index

Subject Categories

Algebra

Copyright

© Jonah N. Henry

Recommended Citation

Henry, Jonah N., "Groups Satisfying the Converse to Lagrange's Theorem" (2019). MSU Graduate Theses. 3452.
https://bearworks.missouristate.edu/theses/3452