A characterisation of large finitely presented groups
A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. In this paper, we give a necessary and sufficient condition for a finitely presented group to be large, in terms of the existence of a normal series where successive quotien...
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| Médium: | Journal article |
| Jazyk: | English |
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Elsevier
2005
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| _version_ | 1826307042533441536 |
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| author | Lackenby, M |
| author_facet | Lackenby, M |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. In this paper, we give a necessary and sufficient condition for a finitely presented group to be large, in terms of the existence of a normal series where successive quotients are finite abelian groups with sufficiently large rank and order. The proof of this result involves an analysis of the geometry and topology of finite Cayley graphs. Theorems of Baumslag and Pride, and their extensions by Gromov and Stohr, on groups with more generators than relations, follow immediately. |
| first_indexed | 2024-03-07T06:57:04Z |
| format | Journal article |
| id | oxford-uuid:fe7ce7bd-7d4d-4db9-9d9a-3b6f886dbc8c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:57:04Z |
| publishDate | 2005 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:fe7ce7bd-7d4d-4db9-9d9a-3b6f886dbc8c2022-03-27T13:36:53ZA characterisation of large finitely presented groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fe7ce7bd-7d4d-4db9-9d9a-3b6f886dbc8cEnglishSymplectic Elements at OxfordElsevier2005Lackenby, MA group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. In this paper, we give a necessary and sufficient condition for a finitely presented group to be large, in terms of the existence of a normal series where successive quotients are finite abelian groups with sufficiently large rank and order. The proof of this result involves an analysis of the geometry and topology of finite Cayley graphs. Theorems of Baumslag and Pride, and their extensions by Gromov and Stohr, on groups with more generators than relations, follow immediately. |
| spellingShingle | Lackenby, M A characterisation of large finitely presented groups |
| title | A characterisation of large finitely presented groups |
| title_full | A characterisation of large finitely presented groups |
| title_fullStr | A characterisation of large finitely presented groups |
| title_full_unstemmed | A characterisation of large finitely presented groups |
| title_short | A characterisation of large finitely presented groups |
| title_sort | characterisation of large finitely presented groups |
| work_keys_str_mv | AT lackenbym acharacterisationoflargefinitelypresentedgroups AT lackenbym characterisationoflargefinitelypresentedgroups |