License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.51
URN: urn:nbn:de:0030-drops-136961
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13696/
Lohrey, Markus
Subgroup Membership in GL(2,Z)
Abstract
It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time where all group elements are represented by so-called power words, i.e., words of the form p_1^{z_1} p_2^{z_2} ⋯ p_k^{z_k}. Here the p_i are explicit words over the generating set of the group and all z_i are binary encoded integers. As a corollary, it follows that the subgroup membership problem for the matrix group GL(2,ℤ) can be decided in polynomial time when all matrix entries are given in binary notation.
BibTeX - Entry
@InProceedings{lohrey:LIPIcs.STACS.2021.51,
author = {Lohrey, Markus},
title = {{Subgroup Membership in GL(2,Z)}},
booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
pages = {51:1--51:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-180-1},
ISSN = {1868-8969},
year = {2021},
volume = {187},
editor = {Bl\"{a}ser, Markus and Monmege, Benjamin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13696},
URN = {urn:nbn:de:0030-drops-136961},
doi = {10.4230/LIPIcs.STACS.2021.51},
annote = {Keywords: free groups, virtually free groups, subgroup membership, matrix groups}
}
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Keywords: |
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free groups, virtually free groups, subgroup membership, matrix groups |
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Collection: |
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38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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10.03.2021 |
