On 𝔍hq-supplemented Subgroups of a Finite Group

Mohamed, M. Ezzat; Al-Shomran, Mohammed M.; Elashiry, M. I.

doi:10.3923/jas.2017.148.152

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2021

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“…The most important structure theorem for finite groups is the Jordan-Holder Theorem, which states that any finite group is built up from finite simple groups. The importance of this structure is that the properties of the subgroups of a given finite group G suggest substantial information about the group G itself such as the nilpotence and the solvability of G, see [3], [1], [5], [4], [21], [16] and [15]. In particular, having the property of simplicity of the group G can be deduced by investigating its subgroups.…”

Section: Introductionmentioning

confidence: 99%

An Application of Finite Groups to Hopf algebras

Almutairi

Al-Shomrani

2021

Eur. J. Pure Appl. Math.

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Kaplanskyâ€™s famous conjectures about generalizing results from groups to Hopf al-gebras inspired many mathematicians to try to find solusions for them. Recently, Cohen and Westreich in [8] and [10] have generalized the concepts of nilpotency and solvability of groups to Hopf algebras under certain conditions and proved interesting results. In this article, we follow their work and give a detailed example by considering a finite group G and an algebraically closed field K. In more details, we construct the group Hopf algebra H = KG and examine its properties to see what of the properties of the original finite group can be carried out in the case of H.

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