Two new criteria for solvability of finite groups

By Marcel Herzog, P. Longobardi, M. Maj. Journal of Algebra, 2018

52 citations recorded by the source corpus.

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 p s . Suppose that A contains a normal cyclic subgroup B satisfying the following condition: A / B is a cyclic group of order 2 r 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 ) ≥ 1 6.68 ψ ( C n ) , where ψ ( G ) denotes the sum of the orders of all elements of G and C n denotes the cyclic group of order n. Then G is a solvable group.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/d5b3f847381ba832c17238d2a61e0a2289e5d6f4

Citations in the corpus

• A criterion for solvability of a finite group by the sum of element orders (2018, unknown): “From the observation that A5 satisfies ψ(A5) = 211 and ψ(C60) = 1617, in [6] they put forward the following conjecture: Conjecture.”