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Classification of involutive commutative two-valued groups
A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated involutive commutative two-valued group is isomorphic to a two-v...
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| Format: | Default Article |
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2022
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| Online Access: | https://hdl.handle.net/2134/22100468.v1 |
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| _version_ | 1818165526305701888 |
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| author | Victor M. Buchstaber Alexander Veselov Alexander A. Gaifullin |
| author_facet | Victor M. Buchstaber Alexander Veselov Alexander A. Gaifullin |
| author_sort | Victor M. Buchstaber (14641024) |
| collection | Figshare |
| description | A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated involutive commutative two-valued group is isomorphic to a two-valued group belonging to one of these series. A number of classification results are obtained for topological involutive commutative two-valued groups in the Hausdorff and locally compact cases. The clas-sification of algebraic involutive two-valued groups in the one-dimensional case is also discussed. |
| format | Default Article |
| id | rr-article-22100468 |
| institution | Loughborough University |
| publishDate | 2022 |
| record_format | Figshare |
| spelling | rr-article-221004682022-07-29T00:00:00Z Classification of involutive commutative two-valued groups Victor M. Buchstaber (14641024) Alexander Veselov (1259028) Alexander A. Gaifullin (14641027) Applied mathematics Mathematical physics Pure mathematics General Mathematics classification of multivalued groups involutive two-valued groups topological groups locally compact groups algebraic two-valued groups <p>A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated involutive commutative two-valued group is isomorphic to a two-valued group belonging to one of these series. A number of classification results are obtained for topological involutive commutative two-valued groups in the Hausdorff and locally compact cases. The clas-sification of algebraic involutive two-valued groups in the one-dimensional case is also discussed.</p> 2022-07-29T00:00:00Z Text Journal contribution 2134/22100468.v1 https://figshare.com/articles/journal_contribution/Classification_of_involutive_commutative_two-valued_groups/22100468 CC BY-NC-ND 4.0 |
| spellingShingle | Applied mathematics Mathematical physics Pure mathematics General Mathematics classification of multivalued groups involutive two-valued groups topological groups locally compact groups algebraic two-valued groups Victor M. Buchstaber Alexander Veselov Alexander A. Gaifullin Classification of involutive commutative two-valued groups |
| title | Classification of involutive commutative two-valued groups |
| title_full | Classification of involutive commutative two-valued groups |
| title_fullStr | Classification of involutive commutative two-valued groups |
| title_full_unstemmed | Classification of involutive commutative two-valued groups |
| title_short | Classification of involutive commutative two-valued groups |
| title_sort | classification of involutive commutative two-valued groups |
| topic | Applied mathematics Mathematical physics Pure mathematics General Mathematics classification of multivalued groups involutive two-valued groups topological groups locally compact groups algebraic two-valued groups |
| url | https://hdl.handle.net/2134/22100468.v1 |