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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.11608 |
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| _version_ | 1866913935413739520 |
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| author | Dogon, Alon Levit, Arie Vigdorovich, Itamar |
| author_facet | Dogon, Alon Levit, Arie Vigdorovich, Itamar |
| contents | We initiate a quantitative study of Hilbert-Schmidt stability for infinitely presented groups through the novel notion of stability radius growth. We exhibit an uncountable family of Hilbert-Schmidt stable amenable groups with arbitrarily large such growth. In particular, this answers a question of Lubotzky. Our approach is based on the character-theoretic stability criterion of Hadwin and Shulman. We classify the characters of alternating and elementary enrichments as well as diagonal products, including the classical family of B.H. Neumann groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characters of diagonal products and Hilbert-Schmidt stability Dogon, Alon Levit, Arie Vigdorovich, Itamar Group Theory 20B07, 20C07, 20C32, 20H20, 47C15, 20C15 We initiate a quantitative study of Hilbert-Schmidt stability for infinitely presented groups through the novel notion of stability radius growth. We exhibit an uncountable family of Hilbert-Schmidt stable amenable groups with arbitrarily large such growth. In particular, this answers a question of Lubotzky. Our approach is based on the character-theoretic stability criterion of Hadwin and Shulman. We classify the characters of alternating and elementary enrichments as well as diagonal products, including the classical family of B.H. Neumann groups. |
| title | Characters of diagonal products and Hilbert-Schmidt stability |
| topic | Group Theory 20B07, 20C07, 20C32, 20H20, 47C15, 20C15 |
| url | https://arxiv.org/abs/2407.11608 |