On the Iwasawa theory of Cayley graphs
arxiv(2024)
Abstract
This paper explores Iwasawa theory from a graph theoretic perspective,
focusing on the algebraic and combinatorial properties of Cayley graphs. Using
representation theory, we analyze Iwasawa-theoretic invariants within
ℤ_ℓ-towers of Cayley graphs, revealing connections between graph
theory, number theory, and group theory. Key results include the factorization
of associated Iwasawa polynomials and the decomposition of μ- and
λ-invariants. Additionally, we apply these insights to complete graphs,
establishing conditions under which these invariants vanish.
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