融合系中态射的扩张问题  

Extension Problems of Morphisms in Fusion Systems

作　　者：郝成功[1] 王霞[1] 常学武[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《中北大学学报（自然科学版）》2015年第6期614-616,625,共4页Journal of North University of China(Natural Science Edition)

基　　金：山西省自然科学基金资助项目(2012011001-1)

摘　　要：探讨了融合系的domestic子群和essential子群的若干等价描述及基本性质.从态射扩张角度刻画了融合系中的Sylow交现象.分析了2010年Craven对一般融合系定义的domestic交,证明了主要结论:设P为有限p-群,F为P上饱和融合系.给定F的一个完全正规化子群Q,则Q为本质子群当且仅当Q存在强不可扩张的F-自同构,Q为domestic子群当且仅当Q存在不可扩张的F-自同构.An exploration was made on some equivalent descriptions and basic properties of the domestic subgroups and essential subgroups of a fusion system.A characterization was presented on maximal Sylow intersections and domestic subgroup which was a new subgroup defined by Craven in 2010 on the point of view of morphism extension.Precisely,the following result is proved：Let Fbe a saturated fusion system on a finite p-group P.A fully normalized subgroup Qis F-essential if and only if Q has a strong non-extendible F-automorphism;Qis a domestic subgroup if and only if Qhas a non-extendible F-automorphism.

关 键 词：融合系 Sylow交 domestic子群 

分 类 号：O152.1[理学—数学]