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arXiv · 1612.01444

The threshold for subgroup profiles to agree is $Ω(\log n)$

James B. Wilson
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Abstract

For primes $p,e>2$ there are at least $p^{e-3}/e$ groups of order $p^{2e+2}$ that have equal multisets of isomorphism types of proper subgroups and proper quotient groups, isomorphic character tables, and power maps. This obstructs recent speculation concerning a path towards efficient isomorphism tests for general finite groups. These groups have a special purpose polylogarithmic-time isomorphism test.

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James B. Wilson. 2016-12-20. The threshold for subgroup profiles to agree is $Ω(\log n)$. https://doi.org/10.4086/toc.2019.v015a019

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