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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Isomorphism in expanding families of indistinguishable groups

Mark L. Lewis / James B. Wilson
Published Online: 2012-05-01 | DOI: https://doi.org/10.1515/gcc-2012-0008


For every odd prime and every integer , there is a Heisenberg group of order that has pairwise nonisomorphic quotients of order . Yet, these quotients are virtually indistinguishable. They have isomorphic character tables, every conjugacy class of a non-central element has the same size, and every element has order at most . They are also directly and centrally indecomposable and of the same indecomposability type. Nevertheless, there is a polynomial-time algorithm to test for isomorphisms between these groups.

Keywords: -group; group isomorphism; polynomial-time; asymptotic group theory

About the article

Received: 2010-10-27

Published Online: 2012-05-01

Published in Print: 2012-05-01

Citation Information: Groups - Complexity - Cryptology, Volume 4, Issue 1, Pages 73–110, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2012-0008.

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