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Isomorphism in expanding families of indistinguishable groups

Isomorphism in expanding families of indistinguishable groups Abstract. 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

Isomorphism in expanding families of indistinguishable groups

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Publisher
de Gruyter
Copyright
Copyright © 2012 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2012-0008
Publisher site
See Article on Publisher Site

Abstract

Abstract. 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.

Journal

Groups - Complexity - Cryptologyde Gruyter

Published: May 1, 2012

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