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Fusion classes of Non-Abelian Metabelian groups of order upto
International Journal of Physics and Mathematics · 2022 · Vol. 4(1) · pp. 61–75
Abstract
In this paper G be the non-abelian metabelian group and denotes the fusion class of element a in G. Fusion class is an equivalence relation. A group is metabelian group if its commutator group is abelian or if it has an abelian normal subgroup in which the factor group is also abelian. There are 35 non-Abelian metabelian groups of order less than or equal to 24. In this paper, we investigate the fusion classes of all non-abelian metabelian groups of order less than or equal to 24 and the verification has been made through GAP(Groups Algorithm Programming) software.
Finite Group Theory ResearchMetabelian groupAbelian groupMathematicsCommutator subgroupElementary abelian groupTorsion subgroupOrder (exchange)Equivalence (formal languages)Rank of an abelian groupPure mathematics
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