# Hierarchical Complexity of Finite Groups

@inproceedings{Nehaniv2021HierarchicalCO, title={Hierarchical Complexity of Finite Groups}, author={Chrystopher L. Nehaniv}, year={2021} }

What are simplest ways to construct a finite group from its atomic constituents? To understand part-whole relations between finite simple groups (“atoms”) and the global structure of finite groups, we axiomatize complexity measures on finite groups. From the Jordan-Hölder theorem and Frobenius-Lagrange embedding in an iterated wreath product, any finite group G can be constructed from a unique collection of simple groups, its Jordan-Hölder factors, each with well-defined multiplicities through…

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