The 2-generator restricted burnside group of exponent 7
We report on our construction of a power-commutator presentation for R(2, 7), the largest finite 2-generator group of exponent 7. Our calculations show that R(2, 7) has order 720416, nilpotency class 28, and derived length 5. The calculations also imply that the associated Lie ring of R(2, 7) satisf...
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Format: | Journal article |
Sprache: | English |
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2002
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author | O'Brien, E Vaughan-Lee, M |
author_facet | O'Brien, E Vaughan-Lee, M |
author_sort | O'Brien, E |
collection | OXFORD |
description | We report on our construction of a power-commutator presentation for R(2, 7), the largest finite 2-generator group of exponent 7. Our calculations show that R(2, 7) has order 720416, nilpotency class 28, and derived length 5. The calculations also imply that the associated Lie ring of R(2, 7) satisfies relations which are not consequences of the multilinear identities which hold in the associated Lie rings of groups of exponent 7. |
first_indexed | 2024-03-07T03:37:02Z |
format | Journal article |
id | oxford-uuid:bca5f88a-0ee8-4b5a-944c-cbc927fba119 |
institution | University of Oxford |
language | English |
last_indexed | 2024-03-07T03:37:02Z |
publishDate | 2002 |
record_format | dspace |
spelling | oxford-uuid:bca5f88a-0ee8-4b5a-944c-cbc927fba1192022-03-27T05:25:51ZThe 2-generator restricted burnside group of exponent 7Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bca5f88a-0ee8-4b5a-944c-cbc927fba119EnglishSymplectic Elements at Oxford2002O'Brien, EVaughan-Lee, MWe report on our construction of a power-commutator presentation for R(2, 7), the largest finite 2-generator group of exponent 7. Our calculations show that R(2, 7) has order 720416, nilpotency class 28, and derived length 5. The calculations also imply that the associated Lie ring of R(2, 7) satisfies relations which are not consequences of the multilinear identities which hold in the associated Lie rings of groups of exponent 7. |
spellingShingle | O'Brien, E Vaughan-Lee, M The 2-generator restricted burnside group of exponent 7 |
title | The 2-generator restricted burnside group of exponent 7 |
title_full | The 2-generator restricted burnside group of exponent 7 |
title_fullStr | The 2-generator restricted burnside group of exponent 7 |
title_full_unstemmed | The 2-generator restricted burnside group of exponent 7 |
title_short | The 2-generator restricted burnside group of exponent 7 |
title_sort | 2 generator restricted burnside group of exponent 7 |
work_keys_str_mv | AT obriene the2generatorrestrictedburnsidegroupofexponent7 AT vaughanleem the2generatorrestrictedburnsidegroupofexponent7 AT obriene 2generatorrestrictedburnsidegroupofexponent7 AT vaughanleem 2generatorrestrictedburnsidegroupofexponent7 |