Abstract
Supersoluble immersion of a normal subgroup K of a finite group G shall be defined by the following property:If σ is a homomorphism of G, and if the minimal normal subgroup J of Gσ is part of Kσ then J is cyclic (of order a prime).Our principal aim in the present investigation is the proof of the equivalence of the following three properties of the normal subgroup K of the finite group G:(i)K is supersolubly immersed in G.(ii)K/ϕK is supersolubly immersed in G/ϕK.(iii)If θ is the group of automorphisms induced in the p-subgroup U of K by elements in the normalizer of U in G, then θ' θp-1 is a p-subgroup of θ.Though most of our discussion is concerned with the proof of this theorem, some of our concepts and results are of independent interest.
Publisher
Canadian Mathematical Society
Cited by
26 articles.
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