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01-Applied Mathematics & Information Sciences
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Volumes > Volume 10 > No. 2

 
   

On Bipermutable and S-Bipermutable Subgroups of Finite Groups

PP: 711-717
doi:10.18576/amis/100231
Author(s)
Awni F. Al-Dababseh,
Abstract
Let H be a subgroup of a finite group G. Then we say that H is: bipermutable in G provided G has subgroups A and B such that G = AB, H ≤ A and H permutes with all subgroups of A and with all subgroups of B; S-bipermutable in G provided G has subgroups A and B such that G = AB, H ≤ A and H permutes with all Sylow subgroups of A and with all Sylow p-subgroups of B such that (|H|, p) = 1. In this paper we analyze the influence of bipermutable and S-bipermutable subgroups on the structure of G.

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