作 者: ;
机构地区: 广东教育学院
出 处: 《广东教育学院学报》 2004年第2期12-14,共3页
摘 要: 在文"Ongeneralizedhypercenterofafinitegroup,Comm.Alg.,29(5),2239-2248(2001)"中,有如下结论:G为超可解当且仅当G=genz∞(G).很自然地,人们猜想:若F (G) genz∞(G),则G为超可解群.给出一个反例说明此猜想的回答是否定的. In this paper, 'On generalized hypercenter of a finite group, Comm. Algebra, 29(5), 2239-2248(2001)', we can find the following argument: a finite group G is supersolvable if and only if G=genz_∞(G), where genz_∞(G) is the super-quasicenter of G. Naturally, we guess: If F~*(G)≤genz_∞(G), where F~*(G) is the generalized Fitting of G, then G is supersolvable. In this paper we give an example to answer this conjecture negatively.