20.500.12556/RUL-140815 Polmer grupe ${\rm SL}_2({\rm F}_p)$ delo diplomskega seminarja Diameter of the group ${\rm SL}_2({\rm F}_p)$ V delu omejimo polmer Cayleyjevega grafa grupe ${\rm SL}_2({\rm F}_p)$. V ta namen predstavimo Helfgottov produktni izrek. Obravnavamo nekaj robnih primerov za zelo majhne in zelo velike generirajoče podmnožice grupe ${\rm SL}_2({\rm F}_p)$. Definiramo maksimalne toruse in regularne polenostavne elemente, preko katerih zapišemo izrek o torusni dihotomiji. Uporabimo tudi izrek o Larsen-Pinkovih neenakostih in si podrobneje ogledamo konjugiranostne razrede grupe ${\rm SL}_2({\rm F}_p)$. In this work, we give an upper bound for the diameter of the Cayley graph of the group ${\rm SL}_2({\rm F}_p)$. For this purpose, we introduce Helfgott's product theorem. We consider some special cases for very small and very large generating subsets of the group ${\rm SL}_2({\rm F}_p)$. We define maximal tori and regular semisimple elements, through which we write down the torus dichotomy theorem. We also present the theorem of Larsen-Pink inequalities and take a closer look at the conjugacy classes of the group ${\rm SL}_2({\rm F}_p)$. Helfgottov produktni izrek torusi regularni polenostavni elementi Helfgott's product theorem tori regular semisimple elements true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2022-09-18 08:15:06 2022-09-18 08:15:07 2024-05-29 12:09:41 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 127404 122434051 5500.pdf 5500.pdf 1 830298BF8A4FE41768E127AD50965FEF 63966d970764c78ef06d2785b9ba9a0c45ba16994f1a0233ebac6ee00c620431 2af10b89-3719-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=161611 Fakulteta za matematiko in fiziko 0 0 0