A Study of Normality by Cayley Graphs and Their Quotients

Ivy, Devin

Here we study the group-theoretic concept of normality by characterizing normal subgroups as they appear within a parent group's Cayley graph. Vertex colorings induce certain combinatorially-defined graph quotients which elucidate the existence or non-existence of normal subgroups. We use this to prove the simplicity of the alternating groups on 5 or more letters. Through vertex-co... read more

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