On Almost Solvable Groups
Received:June 20, 1991  
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Chen Zhongmu Dept. of Math.
Southwest-China Teachers University
Chongqing 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.1993.04.020
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