Quotient sets in nonabelian groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909165431029760 |
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| author | Lev, Vsevolod F. |
| author_facet | Lev, Vsevolod F. |
| contents | We show that for a finite, nonempty subset $A$ of a group, the quotient set $A^{-1}A:=\{a_1^{-1}a_2\colon a_1,a_2\in A\}$ has size $|A^{-1}A|\ge\frac53\,|A|$, unless $A$ is densely contained in a coset, or in a union of two cosets of a finite subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quotient sets in nonabelian groups Lev, Vsevolod F. Group Theory Combinatorics Number Theory 11P70, 11B13 We show that for a finite, nonempty subset $A$ of a group, the quotient set $A^{-1}A:=\{a_1^{-1}a_2\colon a_1,a_2\in A\}$ has size $|A^{-1}A|\ge\frac53\,|A|$, unless $A$ is densely contained in a coset, or in a union of two cosets of a finite subgroup. |
| title | Quotient sets in nonabelian groups |
| topic | Group Theory Combinatorics Number Theory 11P70, 11B13 |
| url | https://arxiv.org/abs/2404.06887 |