On h-Completion for Maximal Subgroups and the
Solvability of Finite Groups
Abstract: In this paper, we propose new definition of an h-completion for a maximal subgroup M of a group G, that is a θ-completion C such that either C = G or there exist a subgroup D of G which is not a θ-completion for M and C < D holds. This method can weaken the imposed maximality on θ-completion. Moreover, we studied the solvability and of finite groups by means of h-completion and obtained some important properties, which are very useful to research deeply finite groups.
文章引用: 张晓燕 , 徐伟华 (2011) 极大子群的h-完备与群的可解性。 理论数学， 1， 124-131. doi: 10.12677/pm.2011.12025
 W. E. Deskin. On maximal subgroups. Proceedings of a Sympo-sium in Pure Mathematics of the American Mathematical Society, 1959, 1: 100-104.
 N. P. Mukherjee, P. Bhattachary. On theta pairs for maximal subgroups. Proceedings of the American Mathematical Society, 1990, 109(3): 589-596.
 Y. Q. Zhao. On the deskins completions, theta completions and theta pairs for maximal subgroups. Communications in Algebra, 1998, 26(2): 3141-3153.
 S. R. Li, Y. Q. Zhao. On s-completions of maximal subgroups of finite groups. Algebra Colloquium, 2004, 11(3): 315-324.
 Y. Q. Zhao. On the deskins completions, theta completions for maximal subgroups. Communications in Algebra, 2000, 28(1): 375-385.
 Y. Q. Zhao. On theta completions & s-completions for maximal subgroups. JP Journal of Algebra, Number Theory and Applications, 2002, 2(2): 111-119.
 徐明耀. 有限群导引[M]. 北京: 科学出版社, 1999.
 T. Hawkes. On the class of Sylow Tower groups. Mathematische Zeitschrift, 1968, 105(5): 393-398.
 B. Huppert, G. I. Endliche. Finite groups. Berlin: Springer-Verlag, 1968.
 J. S. Rose. On finite in solute groups with nipotent maximal subgroups. Journal of Algebra, 1977, 48(4): 182-196.
 Y. Q. Zhao. Completion, theta-completion and the salvability of finite groups. Journal of Applied Algebra and Discrete Structures, 2003, 1(2): 87-97.
 Y. M. Wang. C-normality of groups and properties. Journal of Algebra, 1996, 180(3): 945-965.