New Andrews–Curtis trivializations for Miller–Schupp group presentations
We present recent developments in the applications of automated theorem proving in the investigation of the Andrews–Curtis conjecture. We demonstrate previously unknown trivializations of group presentations from a parametric family MSn(w∗) of trivial group presentations for n=3,4,5,6,7,8 (subset of...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X2400034X |
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| author | Alexei Lisitsa |
| author_facet | Alexei Lisitsa |
| author_sort | Alexei Lisitsa |
| collection | DOAJ |
| description | We present recent developments in the applications of automated theorem proving in the investigation of the Andrews–Curtis conjecture. We demonstrate previously unknown trivializations of group presentations from a parametric family MSn(w∗) of trivial group presentations for n=3,4,5,6,7,8 (subset of well-known Miller–Schupp family). Based on the human analysis of these trivializations we formulate two conjectures on the structure of simplifications for the infinite family MSn(w∗), n≥3. |
| format | Article |
| id | doaj-art-d5e02f28353c47eeb4f037b6c973f05c |
| institution | OA Journals |
| issn | 2666-657X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-d5e02f28353c47eeb4f037b6c973f05c2025-08-20T01:58:31ZengElsevierExamples and Counterexamples2666-657X2024-12-01610016810.1016/j.exco.2024.100168New Andrews–Curtis trivializations for Miller–Schupp group presentationsAlexei Lisitsa0Deaprtment of Computer Science, University of Liverpool, Ashton building, Liverpool, L69 3DR, UKWe present recent developments in the applications of automated theorem proving in the investigation of the Andrews–Curtis conjecture. We demonstrate previously unknown trivializations of group presentations from a parametric family MSn(w∗) of trivial group presentations for n=3,4,5,6,7,8 (subset of well-known Miller–Schupp family). Based on the human analysis of these trivializations we formulate two conjectures on the structure of simplifications for the infinite family MSn(w∗), n≥3.http://www.sciencedirect.com/science/article/pii/S2666657X2400034XCombinatorial group theoryAndrews–Curtis conjectureAC-trivializationsAutomated theorem proving |
| spellingShingle | Alexei Lisitsa New Andrews–Curtis trivializations for Miller–Schupp group presentations Examples and Counterexamples Combinatorial group theory Andrews–Curtis conjecture AC-trivializations Automated theorem proving |
| title | New Andrews–Curtis trivializations for Miller–Schupp group presentations |
| title_full | New Andrews–Curtis trivializations for Miller–Schupp group presentations |
| title_fullStr | New Andrews–Curtis trivializations for Miller–Schupp group presentations |
| title_full_unstemmed | New Andrews–Curtis trivializations for Miller–Schupp group presentations |
| title_short | New Andrews–Curtis trivializations for Miller–Schupp group presentations |
| title_sort | new andrews curtis trivializations for miller schupp group presentations |
| topic | Combinatorial group theory Andrews–Curtis conjecture AC-trivializations Automated theorem proving |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X2400034X |
| work_keys_str_mv | AT alexeilisitsa newandrewscurtistrivializationsformillerschuppgrouppresentations |