The second maximal groups with respect to the sum of element orders

Denote by G a finite group and let ? ( ) denote the sum of element orders in . In 2009, H. Amiri, S.M. Jafarian Amiri I.M. Isaacs proved that if | = n is non-cyclic, then < C , where denotes cyclic order 2018 we non-cyclic ? 7 11 equality holds 4 k with 2 1 × this paper only are as indicated above. Moreover following generalization result: Theorem Let be q being least prime divisor Then ? + 5 Notice