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math.GR2026
A compensation theorem for the Sylow-integral invariant and counterexamples to an \texorpdfstring{}{A5}-characterization conjecture
Yutong Zhang, Yaoran Yang
Let \(ν_p(G)\) be the number of Sylow \(p\)-subgroups of a finite group \(G\), let \(σ_p(G)\) be their common order, and set \[ γ(G)=\int_0^1\sum_{p\inπ(G)}ν_p(G)x^{σ_p(G)}\,dx =\s…
math.GR2026
Finite factorization is detected by undermonoids
Yutong Zhang, Yaoran Yang
Let be a cancellative commutative monoid and call a submonoid of an undermonoid if $\G(S)=\G(M)$ inside the Grothendieck group of . Gotti and Li asked whether the fi…