Date of Graduation
Master of Science in Mathematics
lagrange, group, subgroup, order, index
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.
© Jonah N. Henry
Henry, Jonah N., "Groups Satisfying the Converse to Lagrange's Theorem" (2019). MSU Graduate Theses. 3452.