2019/01/22 by Pedro Henrique Pereira Daldegan, Daldegan, Pedro H. P., Csaba Schneider +1
Mathematics · #Finite Group Theory Research #Rings, Modules, and Algebras #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1901.07285
The first main result of this paper is that a finite transitive nonabelian\ncharacteristically simple subgroup of a wreath product in product action must\nlie in the base group of the wreath product. This allows us to characterize\nnonabelian transitive characteristically simple subgroups H of finite\nquasiprimitive permutation groups G. If the socle of G, denoted by\n\soc(G), is nonabelian, then H lies in \soc(G). An explicit\ndescription is given for the possibilities of H under the condition that H\ndoes not contain a nontrivial normal subgroup of \soc(G).\n