@article{9c2e6aba90dc48a6aea17d119a021e4a,

title = "Two new criteria for solvability of finite groups",

abstract = "We prove the following two new criteria for the solvability of finite groups. Theorem 1: Let G be a finite group of order n containing a subgroup A of prime power index ps. Suppose that A contains a normal cyclic subgroup B satisfying the following condition: A/B is a cyclic group of order 2r for some non-negative integer r. Then G is a solvable group. Theorem 3: Let G be a finite group of order n and suppose that ψ(G)≥[Formula presented]ψ(Cn), where ψ(G) denotes the sum of the orders of all elements of G and Cn denotes the cyclic group of order n. Then G is a solvable group.",

keywords = "Group element orders, Solvable groups",

author = "Marcel Herzog and Patrizia Longobardi and Mercede Maj",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2018",

month = oct,

day = "1",

doi = "10.1016/j.jalgebra.2018.06.015",

language = "אנגלית",

volume = "511",

pages = "215--226",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}