Some Groups That Satisfy the Converse to Lagrange's Theorem

In response to a viewer question, we discuss some classes of groups for which the converse to Lagrange's theorem holds. We explicitly prove that the converse holds for all cyclic groups, explain why this extends to abelian groups, and also mention the relationship with the classes of solvable, supersolvable, and p-groups.

[theillusionzone]

2:26 Great video, just a minor question, you say that "m divides n". But then you write "n/m is an integer", but for m>n, n/m cannot be an integer (as it will be less than 1). Sorry I'm confused, did you mean to write 'n divides m' instead?