Abstract
AbstractA complete Sylow sequence, 𝒫=P1,…,Pm, of a finite group G is a sequence of m Sylow pi-subgroups of G, one for each pi, where p1,…,pm are all of the distinct prime divisors of |G|. A product of the form P1⋯Pm is called a complete Sylow product of G. We prove that the solvable radical of G equals the intersection of all complete Sylow products of G if, for every composition factor S of G, and for every ordering of the prime divisors of |S|, there exist a complete Sylow sequence 𝒫 of S, and g∈S such that g is uniquely factorizable in 𝒫 . This generalizes our results in Kaplan and Levy [‘The solvable radical of Sylow factorizable groups’, Arch. Math.85(6) (2005), 490–496].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.