CAJ | 학술논문

设F是由f(p)所局部定义的可解群系,G∈F,A是ZG-模.我们称A的一个p-主因子U/V在G中是F-中心的,如果G/CG(U/V)∈f(p).否则称U/V在G中是非中心的.本文证明了:设G是超-(有限或循环)的局部可解群,A是Artinian ZG-模且所有的不可约ZG-因子都是有限的;F为由f(p)所局部定义的局部可解群系,且对任意的p∈π,f(p)≠φ,f(∞) f(p).如果G∈F,且A的所有不可约ZG-因子在G中均是F-非中心的,则A被G的扩张在A上共轭可裂..
설F시유f(p)소국부정의적가해군계,G∈F,A시ZG-모.아문칭A적일개p-주인자U/V재G중시F-중심적,여과G/CG(U/V)∈f(p).부칙칭U/V재G중시비중심적.본문증명료:설G시초-(유한혹순배)적국부가해군,A시Artinian ZG-모차소유적불가약ZG-인자도시유한적;F위유f(p)소국부정의적국부가해군계,차대임의적p∈π,f(p)≠φ,f(∞) f(p).여과G∈F,차A적소유불가약ZG-인자재G중균시F-비중심적,칙A피G적확장재A상공액가렬..
Let F be a formation locally defined by f(p), G∈ F and A a ZG-module, where p∈π= {all primes and ∞}. Then a p-main-factor U/V of is said to be F-central in G, if G/CG(U/V)∈f(p). Otherwise, it is said to be F-eccentric in G. In this paper, the following results are proved: Let F be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite, if G∈F, f(∞) f(p),f(p)≠φ for each p∈π and all irreducible ZG-factors of A are F-eccentric in G, then any extension E of A by G splits conjugately over A.