GENERIC COMPLEXITY OF THE CONJUGACY PROBLEM IN HNN-EXTENSIONS AND ALGORITHMIC STRATIFICATION OF MILLER'S GROUPS-Reference-Cited by-同舟云学术

GENERIC COMPLEXITY OF THE CONJUGACY PROBLEM IN HNN-EXTENSIONS AND ALGORITHMIC STRATIFICATION OF MILLER'S GROUPS

Published:2007-08 Issue:05n06 Volume:17 Page:963-997
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

BOROVIK ALEXANDRE V.¹,MYASNIKOV ALEXEI G.²,REMESLENNIKOV VLADIMIR N.³

Affiliation:

1. School of Mathematics, PO Box 88, The University of Manchester, Sackville Street, Manchester M60 1QD, United Kingdom

2. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St W., Montreal, QC, H3A 2K6, Canada

3. Omsk Branch of Mathematical Institute SB RAS, 13 Pevtsova Street, Omsk 644099, Russia

Abstract

We discuss time complexity of the Conjugacy Problem in HNN-extensions of groups, in particular, in Miller's groups. We show that for "almost all", in some explicit sense, elements, the Conjugacy Problem is decidable in cubic time. It is worth noting that the Conjugacy Problem in a Miller group may be undecidable. Our results show that "hard" instances of the problem comprise a negligibly small part of the group.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196707003913

Reference26 articles.

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