陈重穆.关于几乎可解群[J].数学研究及应用,1993,13(4):579~581
关于几乎可解群
On Almost Solvable Groups
投稿时间:1991-06-20  
DOI:10.3770/j.issn:1000-341X.1993.04.020
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英文关键词:
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作者单位
陈重穆 西南师范大学 
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中文摘要:
      本文推广了关于局部有限群的Asar定理及p.Hall—Kulatilaka,Kargapolov定理.
英文摘要:
      Group G is called almost solvable, if G has a finite normal series such that each factor group of the series is abelian or finite. We show that(1) If locally almost solvable period group G has a finite Sylow p-subgroup, then all Sylow p-subgroups of G are finite and conjuate.(2) Every infinite locally almost solvable group has an infinite abelian subgroup.(3) Suppose that the Sylow p-subgroups of G are locally finite and every finitely generated subgroup of G possesses the "Sylow finite p- property". That is, each finite p-subgroup is isomorphic to some subgroup of each Sylow p-subgroup. If each countable subgroup of G has only countably many Sylow p-subgroups, then all the Sylow p-subgroups of G are conjugate.
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