Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph Invariants of Finite Groups via a Theorem of Lagarias   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. In particular,
each connected component corresponds to a division (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.

26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph