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Isomorphism in expanding families of indistinguishable groups
-
Mark L. Lewis
and
James B. Wilson
Published/Copyright:
May 1, 2012
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.
Received: 2010-10-27
Published Online: 2012-05-01
Published in Print: 2012-May
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Two-party key establishment: From passive to active security without introducing new assumptions
- Continuous hard-to-invert functions and biometric authentication
- Existence, algorithms, and asymptotics of direct product decompositions, I
- Isomorphism in expanding families of indistinguishable groups
- Search and test algorithms for triple product property triples
- Evolutionary algorithm solution of the multiple conjugacy search problem in groups, and its applications to cryptography
- A Diffie–Hellman key exchange protocol using matrices over noncommutative rings
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