An elementary approach for a description of the Fitting subgroup and soluble radical of a finite group G
DOI:
https://doi.org/10.35819/remat2021v7i2id5193Keywords:
Group, Nilpotent Groups, Soluble Groups, Fitting Subgroup, Soluble RadicalAbstract
This work presents an approach that prioritizes the use of Isomorphism Theorems of Groups to study soluble groups and nilpotent groups, which aim to describe the soluble radical S(G) of a finite group G as the largest normal solvable subgroup of G and the Fitting subgroup F(G) of a finite group G as the largest normal nilpotent subgroup of a finite group G. As an application, we show that this description allow us to verify whether S(G) and F(G) are examples of a subgroup class defined in Deaconescu and Walls (2011) for which there is a generalization of a classic result that relates a group G with its automorphism group Aut(G).
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