Minimal non-abelian groups with an average condition on subgroups

For a finite group G, the average order   o(G)   is defined to be the average of all order elements in G. We say that G satisfies the average condition if o(H)\leq o(G) for all subgroups H of G. In [On a question of Jaikin-Zapirain about the average order elements of finite groups, Int. J. Group Theory, To appear] we proved that every abelian group satisfies the average condition. In this paper, we classify minimal non-abelian groups which satisfy the average condition.

کلیدواژه ها:

‎Minimal non-abelian groups ، ‎Group element orders ، ‎Sum of element orders ، ‎Average condition