## Tensor quasi-random groups

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Mark Sellke
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**9**(2022), 12-21

## Abstract:

Gowers [Combin. Probab. Comput. 17 (2008), pp. 363–387] elegantly characterized the finite groups $G$ in which $A_1A_2A_3=G$ for any positive density subsets $A_1,A_2,A_3$. This property,*quasi-randomness*, holds if and only if $G$ does not admit a nontrivial irreducible representation of constant dimension. We present a dual characterization of

*tensor quasi-random*groups in which multiplication of subsets is replaced by tensor product of representations.

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## Additional Information

**Mark Sellke**- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- MR Author ID: 988911
- ORCID: 0000-0001-9166-8185
- Email: msellke@stanford.edu
- Received by editor(s): August 20, 2020
- Received by editor(s) in revised form: March 19, 2021
- Published electronically: February 7, 2022
- Communicated by: Martin Liebeck
- © Copyright 2022 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B
**9**(2022), 12-21 - MSC (2020): Primary 20C15
- DOI: https://doi.org/10.1090/bproc/86
- MathSciNet review: 4377265