Gábor Somlai

activity

20132026

most citedThe Cayley isomorphism property for

Z_{p}^{3} \times Z_{q}

4 citations · 6 across the 9 of their papers we have counts for

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5 papers · 1 filter

math.CA2024

Spectrality of the product does not imply that the components are spectral

Gábor Somlai

Greenfeld and Lev conjectured that the Cartesian product of two sets $A$ and $B$ is spectral if and only if $A$ and $B$ are spectral. We construct a counterexample to this fact usi…

math.CA2023

Spectral Tile Direction in the Group $Z_{p^{2}} \times Z_{q^{2}} \times Z_{r}$

Thomas Fallon, Gergely Kiss, Azita Mayeli +1

Let $p$ , $q$ , and $r$ be distinct primes such that $p^{2} q^{2} < r$ . We prove that every spectral set in the cyclic group $Z_{p^{2} q^{2} r}$ is a tile. Since the reverse direction is…

math.CA2021★ 2 cited

Spectral sets and tiles in $Z_{p}^{2} \times Z_{q}^{2}$

Thomas Fallon, Gergely Kiss, Gábor Somlai

In this paper we study Fuglede's conjecture on the direct product of two cyclic groups. After collecting the known results we prove that Fuglede's conjecture holds on $\mathbb{Z}_{…

math.CA2019

Fuglede's conjecture holds on $Z_{p}^{2} \times Z_{q}$

Gergely Kiss, Gábor Somlai

The study of Fuglede's conjecture on the direct product of elementary abelian groups was initiated by Iosevich et al. For the product of two elementary abelian groups the conjectur…

math.CA2018

On the discrete Fuglede and Pompeiu problems

Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai +1

We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric conditio…

Spectrality of the product does not imply that the components are spectral

Spectral Tile Direction in the Group Zp2​×Zq2​×Zr​

Spectral sets and tiles in Zp2​×Zq2​

Fuglede's conjecture holds on Zp2​×Zq​

On the discrete Fuglede and Pompeiu problems

Spectral Tile Direction in the Group $Z_{p^{2}} \times Z_{q^{2}} \times Z_{r}$

Spectral sets and tiles in $Z_{p}^{2} \times Z_{q}^{2}$

Fuglede's conjecture holds on $Z_{p}^{2} \times Z_{q}$