JP Journal of Algebra, Number Theory and Applications
Volume 8, Issue 2, Pages 227 - 258
(August 2007)
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GRAPH INVARIANTS OF FINITE GROUPS VIA A THEOREM OF LAGARIAS
F?kman (U. S. A.)
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Abstract: We introduce a new graph invariant of finite groups that provides a complete characterization of the splitting types of unramified prime ideals in normal number field extensions entirely in terms of the Galois group.Inparticular,each connectedcomponent correspondsto adivision (Abteilung) of the group. We compute the divisions of the alternating group, and compile a list of characteristics of groups that the invariant reveals. We conjecture that the invariant distinguishes finite groups. Our exposition borrows elements from graph theory, group theory, and algebraic number theory. |
Keywords and phrases: graph invariants, finite groups, algebraic number theory, Galois theory, graph theory, ring of algebraic integers. |
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