Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895809 | Journal of Algebra | 2018 | 13 Pages |
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 Ï(G)â¥16.68Ï(Cn), where Ï(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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marcel Herzog, Patrizia Longobardi, Mercede Maj,