Author

Yi-Nan Li

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Preprint Oct 2026

Almost tight asymptotic enumeration of finite $p$-groups: Almost all finite groups are $2$-groups of class $2$

Let $f(n)$ denote the number of isomorphism classes of groups of order $n$. We prove, uniformly over all primes $p$, that \[ \log_p f(p^m)=\frac{2}{27}m^3-\frac49m^2+O(m), \] with an absolute implied constant. This improves the classical upper bounds of Sims (\emph{Proc. Lond. Math. Soc.}, 1965) and Newman--Seeley and...

Yi-Nan Li, You-Ming Qiao · 0 citations

Preprint Sep 2026

Improved Quantum Algorithms for Black-Box Abelian Group Decomposition

Decomposing finite Abelian black-box groups into cyclic factors is a basic problem in quantum computation. We give a quantum algorithm for decomposing finite Abelian black-box groups by adapting the quantum sampling and classical lattice-reduction method of Regev's factoring algorithm. The algorithm computes an invaria...

Jun Luo, Yi-Nan Li, François Le Gall · 0 citations