Concise presentations of direct products
Direct powers of perfect groups admit more concise presentations than one might naively suppose. If H1(G;Z) = H2(G;Z) = 0, then Gn has a presentation with O(log n) generators and O(log n)3 relators. If, in addition, there is an element g 2 G that has infinite order in every non-trivial quotient of G...
| Tác giả chính: | |
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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
| Được phát hành: |
American Mathematical Society
2022
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| _version_ | 1826294697865248768 |
|---|---|
| author | Bridson, M |
| author_facet | Bridson, M |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | Direct powers of perfect groups admit more concise presentations than one might naively suppose. If H1(G;Z) = H2(G;Z) = 0, then Gn has a presentation with O(log n) generators and O(log n)3 relators. If, in addition, there is an element g 2 G that has infinite order in every non-trivial quotient of G, then Gn has a presentation with d(G) + 1 generators and O(log n) relators. The bounds that we obtain on the deficiency of Gn are not monotone in n; this points to potential counterexamples for the Relation Gap Problem. |
| first_indexed | 2024-03-07T03:49:41Z |
| format | Journal article |
| id | oxford-uuid:c0c95a8f-e731-492b-bd2e-af4d0e1904e6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:49:41Z |
| publishDate | 2022 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:c0c95a8f-e731-492b-bd2e-af4d0e1904e62022-03-27T05:57:03ZConcise presentations of direct productsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c0c95a8f-e731-492b-bd2e-af4d0e1904e6EnglishSymplectic Elements at OxfordAmerican Mathematical Society2022Bridson, MDirect powers of perfect groups admit more concise presentations than one might naively suppose. If H1(G;Z) = H2(G;Z) = 0, then Gn has a presentation with O(log n) generators and O(log n)3 relators. If, in addition, there is an element g 2 G that has infinite order in every non-trivial quotient of G, then Gn has a presentation with d(G) + 1 generators and O(log n) relators. The bounds that we obtain on the deficiency of Gn are not monotone in n; this points to potential counterexamples for the Relation Gap Problem. |
| spellingShingle | Bridson, M Concise presentations of direct products |
| title | Concise presentations of direct products |
| title_full | Concise presentations of direct products |
| title_fullStr | Concise presentations of direct products |
| title_full_unstemmed | Concise presentations of direct products |
| title_short | Concise presentations of direct products |
| title_sort | concise presentations of direct products |
| work_keys_str_mv | AT bridsonm concisepresentationsofdirectproducts |