Twisted conjugacy classes in twisted Chevalley groups
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916985875464192 |
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| author | Bhunia, Sushil Dey, Pinka Roy, Amit |
| author_facet | Bhunia, Sushil Dey, Pinka Roy, Amit |
| contents | Let G be a group and ϕ be an automorphism of G. Two elements x, y of G are said to be ϕ-twisted if y = gxϕ(g)^{-1} for some g in G. We say that a group G has the R_{\infty}-property if the number of ϕ-twisted conjugacy classes is infinite for every automorphism ϕ of G. In this paper, we prove that twisted Chevalley groups over the field k of characteristic zero have the R_{\infty}-property as well as S_{\infty}-property if k has finite transcendence degree over \mathbb{Q} or Aut(k) is periodic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_01446 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Twisted conjugacy classes in twisted Chevalley groups Bhunia, Sushil Dey, Pinka Roy, Amit Group Theory 20E45 Let G be a group and ϕ be an automorphism of G. Two elements x, y of G are said to be ϕ-twisted if y = gxϕ(g)^{-1} for some g in G. We say that a group G has the R_{\infty}-property if the number of ϕ-twisted conjugacy classes is infinite for every automorphism ϕ of G. In this paper, we prove that twisted Chevalley groups over the field k of characteristic zero have the R_{\infty}-property as well as S_{\infty}-property if k has finite transcendence degree over \mathbb{Q} or Aut(k) is periodic. |
| title | Twisted conjugacy classes in twisted Chevalley groups |
| topic | Group Theory 20E45 |
| url | https://arxiv.org/abs/2002.01446 |