西南石油大学学报(自然科学版) ›› 1996, Vol. 18 ›› Issue (4): 107-109.DOI: 10.3863/j.issn.1000-2634.1996.04.022
• 管理科学、基础科学 • 上一篇 下一篇
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TU Dao-xing
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摘要: 设G为有限群,π为某素数集合。G的子群H称为G的π—S—拟正规子群,如果对每个P∈π,H与G的每个Sylow P—子群可换。G称为Bp群,如果NG(P)为P-幂零群蕴含G为P-幂零群,其中P∈SylpG。本文证明了G为Pp群,如果G满足下列条件之一:(1)G的Sylow P—子群P的每个极大子群为G的p—S—拟正规子群;(2)G的Sylow P—子群P的每个二次极大子群为G的p—S—拟正规子群。
关键词: 有限群, 西洛子群, 正规子群
Abstract: Let G be a finite group, and let be a set of primes. A subgroup H of G is calledπ-S-quasi-normal in G if H is permuted with every Sylow p-subgroup of G for every p inπ. G is called a Bpgroup if the existence of normal p-complements of N (P) implies that G itself as a normal p-complement, where PE Sylp G . In this paper, we have proved that G is a Bpgroup if G satisfies one of the following conditions: (1) each maximal subgroup of a Sylow p-subgroup P of G is P’-S-quasi-mormal in G ; (2) each second maximal subguoup of a Sylow p- subgroup P of G is p’-S-quasi-normal in G .
Key words: Finite groups, Sylow subgroups, Normal subgroups
中图分类号:
O152.1
涂道兴. 有限群为Bp群的两个充分条件[J]. 西南石油大学学报(自然科学版), 1996, 18(4): 107-109.
TU Dao-xing. Two Sufficient Conditions for a Finite Group as BpGroup [J]. 西南石油大学学报(自然科学版), 1996, 18(4): 107-109.
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