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Free Content A Typology for Finite Groups

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Abstract:

This project classifies groups of small order using a group's center as the key feature. Groups of a given order n are typed based on the order of each group's center. Students are led through a sequence of exercises that combine proof-writing, independent research, and an analysis of specific classes of finite groups (including the dihedral, symmetric, and alternating groups) to produce a list of groups of each possible type. The project can serve as a capstone experience that unifies group theory with expository mathematical writing.

Document Type: Research Article

DOI: https://doi.org/10.4169/college.math.j.44.5.432

Publication date: 2013-11-01

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