The conjugacy problem in amalgamated products I: Regular elements and black holes

Alexandre V. Borovik; Alexei G. Myasnikov; Vladimir N. Remeslennikov

doi:10.1142/S0218196707003652

The conjugacy problem in amalgamated products I: Regular elements and black holes

Alexandre V. Borovik
, Alexei G. Myasnikov
, Vladimir N. Remeslennikov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We discuss the time complexity of the word and conjugacy search problems for free products G = A *_C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the conjugacy search problem is decidable under some reasonable assumptions about groups A, B, C.

Original language	English
Pages (from-to)	1299-1333
Number of pages	35
Journal	International Journal of Algebra and Computation
Volume	17
Issue number	7
DOIs	https://doi.org/10.1142/S0218196707003652
State	Published - Nov 2007

Keywords

Amalgamated problem
Conjugacy problem
Group

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10.1142/S0218196707003652

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abstract = "We discuss the time complexity of the word and conjugacy search problems for free products G = A *C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the conjugacy search problem is decidable under some reasonable assumptions about groups A, B, C.",

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KW - Amalgamated problem

KW - Conjugacy problem

KW - Group

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JO - International Journal of Algebra and Computation

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The conjugacy problem in amalgamated products I: Regular elements and black holes

Abstract

Keywords

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