Abstract:

 

The order sequence of a finite group $G$ is the list of orders of its elements, arranged in non-decreasing order. Order sequences of groups of order  $n$  are compared by elementwise domination, forming a partially ordered set. In this talk, we demonstrate that this poset has a unique maximal element, corresponding to the cyclic group. This result confirms Problem 18.1 in the Kourovka Notebook (Unsolved Problems in Group Theory, 18th ed).