【摘要】 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)≠ ,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 . .更多还原

【Abstract】 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/C G(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)≠ 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.更多还原